Character Relationships and Personality
Ranma
In general Ranma is pretty easy going, and he is a lot more tolerant than most of the cast. He also will protect anyone is danger, being bullied on (even if they're normally strong, or are his enemy), and helps out people with their problems. He is rarely underhanded and sneaky (though he is good at it when pushed to use it) nor vindictive (but if you really piss him off, you'll be in deep shit) and is pretty open, honest and direct, and feels bad when he did something he knew he shouldn't.
However, it is quite hard to get a real idea of what he thinks, and how he really behaves, even though Ranma is of course the main character, so good examples are few and far between. This is mostly because Ranma is not the introspective type and so we hardly get any pondering of his situation in general, and also because he occasionally does some very surprising things. However, it seems that most of the latter he does on impulse - ie he gets an idea on how to resolve something and immediately does it, even though if he thought about it more he would reject it - most likely for being too embarrassing or strange.
Ranma has had quite an unusual life, and this helps explain many things about him. For example, his only constant companion has been his father, as he probably moves around quite a bit, and Ranma doesn't seem to want any close friends, or open up to people. So Ranma doesn't consider how his actions might be viewed by others, and he has a very straight and direct attitude, in that he rarely hides his opinions or his feelings about a particular subject, or takes into account how others might react to it. In other words, he's insensitive, and over-honest, and often says things he shouldn't have. This is why he has so much trouble dealing with Akane, because not only does he often accidently insult her (since she has quite a few faults, this isn't hard), but he ignores how his actions or behaviour would effect Akane, and of course he also deliberately insults her when they argue - though from his point of view, he didn't start it.
Akane
Like Ranma, she often helps out people with their problems (has even helped out Shampoo, Mousse and Ukyö), honest, and rarely uses underhanded tricks and isn't exactly vindictive. Sometimes she can be a little cruel, but only when she feels quite put upon.
However, she does get angry quite easily, and violent especially towards boys, but once she calms down again, she's normally okay again - it isn't often she stays angry with someone for long. She does also have a particular problem in believing Ranma though, and generally expects the worst of him and doesn't give him time to explain his actions.
Relationship between Akane and Ranma.
At the beginning, he didn't seem to like her much (just thought she was a stupid macho girl mostly - though he did occasionally see her in a complementary manner). However for the entire series he has been protective of her, and will always defend her from physical harm or attacks in general (not matter the cost to himself) or from other males. For example, every time Ryöga might get a chance to be alone with Akane, Ranma always interferes (mostly using a girl-disguise which Ryöga never sees through). Also when Ranma thought Akane loved Shinnosuke and would even risk death for him, he was still prepared to give his life to save Akane (even though he was upset at her for dumping him) and was even willing to leave her so she could be happy.
Ranma will always play down his relationship with Akane, and would normally never say or try to give the impression that he has strong feelings for Akane, or wants to marry her. Often when it's pointed out that some action of his indicated love, or when someone says he loves Akane, he will get very embarrassed and very strenuously deny it, to the point of overkill - if Akane's around, she'll often hit him for this. In more intimate moments with Akane, Ranma is often a little confused (by Akane's actions), embarrassed (even if he's acting quite determinedly) and a little uncertain about what to do. In other words, he gets flustered, although this doesn't paralyse him.
For normal everyday encounters, Ranma and Akane sit side by side at the table, in class, often walk to and from school together and often go places together - they drop in at 'Ucchan's" together occasionally, and at festivals they're often together, though not necessarily alone. They are comfortable with each others presence, and are quite capable of having normal polite conversation, but due to lack of evidence it's hard to get a fix on what they're really like for most of the time. This is because the plots are because of unusual situations, and we rarely get glimpses of everyday situations.
Like with Ranma, on the surface Akane doesn't seem to want to marry Ranma, and almost always denies she has strong feelings for him or that she wants to marry him. At the beginning of the series, Akane loved Dr Tofü, and hated all the other boys for being complete jerks (the only relationship she seemed to have with boys was beating the fools up in the morning), so Ranma would be less likely to be well thought of - for a start, she wanted to marry Dr Tofü, not Ranma. The way Akane finds out about Ranma (ie seeing him naked in the bath), the way he's suddenly engaged to her (forcibly and out of the blue) and his attitude, all would make it less likely for her to like Ranma and hate him instead. However, Akane's one-way relationship with Dr Tofü ended, and it could be that Ranma being there helped (take her mind off it at the least), and also she probably started to respect Ranma a little for his fighting ability, and maybe she was happy to have a fiancée who was good looking, and so much better than the other young martial artists.
Unfortunately for her, Ranma suddenly gets more fiancées, which does not please her at all (showing she does care about their relationship) and it is a slight against her (which Ranma gets blamed for, though it isn't entirely his fault), and it makes it worse that the other girls are mostly 'better' than she is, in looks cooking ability, combat etc.
As the series progresses, they both get slowly closer towards each other. Ranma might cause a lot of problems for Akane, but he does help her out, and it appears she slowly begins to respect him more and more for his determination and fighting ability, and she also is probably happy to have a fiancée who is at least a little handsome, he can be pretty cool sometimes and she probably also realises that he isn't really interested in other girls.
For example, when Pantyhose kidnaps her and lights a signal for the others to find, she tells him not to underestimate Ranma (V18.4), when Ranma is permanently cursed female, she's happy to see Ranma her normal determined and confident self as Ranma prepares to chase after Herb (V24.3) and when Asuka says Ranma has no looks etc. (V32.6) she gets angry, and makes Ranma dress up nice, and even forces him to go on a date with Kodachi, so that she can demonstrate that she has a cool fiancée.
Much is made of their arguments, but from the available evidence, most of their arguments stem from anything that would hit upon their relationship in any way. Eg Ranma seemingly being interested in other girls, being rude to Akane, being a pervert, or things that would hint about their relationship (ie anything to do with normal couple's activities), or when Akane shows again that she's not that good at normal feminine activities. Their arguments sometimes start from little, but Ranma is a bit insensitive (can be pretty bad at times, though he often realises it later) and has this amazing ability to say something which is (or mostly is) true, but in a very direct and insulting way though he probably doesn't mean it as much as he intends or at all.
This often results in Akane beating up his face a little, hammering on the head, or kicking him into the distance though rarely to the tune of 'Ranma no baka' as some fan-fics might have you believe - she often thinks of him as a 'baka' when he isn't around. Because Akane has a flash-fire temper, their arguments are often over very quickly, and since Akane is reasonably forgiving (once she's calmed down and knows the whole story) then things will be back to normal. Unfortunately, it is hard to figure out just how much they argue under normal circumstances as we don't see enough of this. However, they certainly don't fight all the time, or even most of the time, maybe about once a day, if that.
Genma Saotome
In some ways, Genma is a more extreme version of his son - he is even more insensitive than Ranma, and is also very self-centred. For example he wanted to raise Ranma to be a strong martial artist, but doesn't seem to care how his methods have effected Ranma. He removed Ranma from his mother, and doesn't care about how this effected Nodoka, or how his stupid promise to her torments Ranma now. Also, Genma also stole food from Ranma (even when he was a child) and they still fight over it now. He also engaged Ranma to one of Soün's daughters, and later also engaged him to Ukyö, then dumped her, just because he was greedy.
He has made other stupid promises with little regard to how they effect others - for example, he and Soün lost a food eating contest to the Picollet's, and they both promised a daughter to them. Genma is also a petty thief, lazy, a coward, more than a bit stupid and often makes Ranma a scape-goat, and rarely helps him when he has his own problems.
Ranma and Genma don't get along particularly well - they fight all the time, and often casually beat each other up. Also, the Tendö sisters and others don't have much respect for him, and often expect the worst of him. Genma does recognise his responsiblities as a martial artist in that he helps out the general public when it is needed, but he doesn't seem to take it that seriously or believe in it. For example, in one story, Genma, Ranma and Soün goto a town to help out with a problem, but Ranma is the only one who does anything, while the other two try can con the villages out as much as possible, and generally laze around.
Nodoka Saotome
Rather like Kasumi, Nodoka is a calm, quite and kind person, though she does take her responsibilities as a martial artist's wife very seriously, and also has a strong sense of justice - like Ranma. Though she does have a gentle personality, if circumstances require it, she will wield her sword, and will attack using it. She also treats 'Ranko' and Akane as would a mother, or close relation would. She deeply misses Ranma, and would very much like to see him, no matter what.
Soün Tendö
Like Genma, he is insensitive (eg engaging his daughters to various people without telling them), and a coward, lazy and a bit stupid and appears to be a bit oblivious like Kasumi to many of the stranger events in his household, though he is a bit kinder than Genma. He also over-reacts to various situations (rather like Akane), and will either start crying or get very mad (generally at Ranma). To other people he is polite and kind, and like Genma doesn't seem to truely believe in his responsibilities as a martial artist, but he does help out people, though he misses out on the danger signs indicating the problem might be a lot worse than it might appear at first.
Nabiki Tendö
Another self-centred and insensitive character, she often deliberately lies either for the fun of it (generally to tease someone else like Ranma, Akane or Kunö), or to make money, or to get out of a situation. She is a cold, analytical type, who doesn't have a girl's heart, and is only concerned about her own interests - making fun of people, making money, snaking etc.
Kasumi Tendö
Even though she's only 19, she is very much a quiet, kind and gentle motherly person, who is quite selfless. She is also very stable, and calm in a crisis or in the face of something shocking. However, she does occasionally get angry with others - typically Ranma when he's upset Akane again, or her father when he's done something stupid again. While she does often seem quite oblivious to whats going on, she is not living in her own rose-tinted world - for example, she saw right through Nabiki pretending to love Ranma.
Dr Ono Tofü
Another calm, and quiet character, though he is quite serious most of the time, but he does like play the odd small joke. As well as healing people as part of his job as a doctor, he also helps people out with other problems where his expertise can be applied.
Tatewaki Kunö
A very obsessive, arrogant, stuck-up, insensitive and stupid person. His is almost completely ignorant of what others may want or need, and generally just ignores what he doesn't want to see, and looks at the would in a very peculiar way. Others generally regard him as pretty stupid (especially Ranma), and don't have much respect for him - though the some of the school students are a little afraid of him.
Kodachi Kunö
Obsessive, and arrogant like her brother, she is also a delinquent and never even considers fair play, and goes for what she wants without any consideration of how it would effect others - eg she wants to possess Ranma, and she doesn't care how. She is also better than her brother at understanding people's feelings - for example, she does know that Ranma doesn't love her.
Principal Kunö
Another crazy Kunö, he enjoys making life hell for the students, and being a general pain in the ass, and often mocks people.
Shampoo
Although she can sometimes be nice, she can also be cruel, insensitive, obsessive and has a violent temper and nature. For example, she's often mean to Mousse, goes after Ranma with anything she can use, and doesn't really seem to care what he thinks of her for this. In general, she prefers to use violence or trickery to get her way, and isn't merciful to anyone getting in the way.
She is very forward towards Ranma, and often clutches/clomps onto Ranma without any consideration of the situation. She generally ignores Mousse, but does get annoyed when he mistakes other things/people for her, and has spied on him a few times, which shows that she has some feelings for him, and has even been on dates with him.
Mousse
Like Shampoo, he is obsessive and violent, and will be underhanded, and is prepared to use extreme measures to get what he wants - Shampoo, who is the only person he is ever truely nice to (though he isn't impolite to others in general), and he doesn't have any friends. His whole life revolves around Shampoo, and he gets ecstatic whenever he thinks she's being nice to him.
Cologne
Rather cold-blooded and a bit cruel, she also will use underhanded tricks, or force to get what she wants (generally trying to get Ranma marry Shampoo), but she will often help out with people's problems, though she may demand a high price sometimes.
Happosai
Extremely obsessed with girls' bodies and underwear, he is also rather unforgiving and a bit evil. He particularly targets onna-Ranma and Akane, and will use magic, force, underhanded tricks and just about anything else to get what he wants. Happosai considers himself to be Ranma's master, and expects him to behave accordingly, but Ranma never has - most likely because Happosai likes splashing Ranma with water, and enjoying the results.
Ryöga Hibiki
Another obsessive type, Ryöga is also particularly dim-witted, and is pretty unreasonable - particularly blaming things on Ranma, when it isn't really his fault, and has a bad temper. His is also particularly shy around girls, and gets a bad nose-bleed when he sees a girl's naked body, and in related situations. Though he does really love Akane, and often tries to work up the courage to tell her, he can stray if any girl appears to want him (ie onna-Ranma in disguise).
In a similar way to Ranma and Akane, he also has a sense of honour and fair-play - for example, he helps Ranma when he lost his strength because of Happosai. He is also rather protective of Akane, and is sensitive to her feelings, and gets quite upset when Ranma appears to be playing around with girls again, and pretty much hates Ranma generally.
Ukyö Kuonji
Although she did spend 10 years waiting to get revenge on Ranma and Genma for dumping her, she is not particularly obsessive, and is generally friendly and cheerful to everyone. Though she is sometimes a little sneaky - generally in trying to separate Ranma and Akane, instead of using force. She is also a bit protective of Ranma (ie sometimes attacks people who attack Ranma), but she also gets upset when Ranma appears to be going after other girls. Although she loves Ranma, she is a bit shy about it, but she would still want to marry Ranma even if he was weak or very poor.
Hinako Hinomiya
Having a split-personality often causes her difficulties in trying to what task is at hand - eg her students aren't particularly afraid of her (except when she starts using her special powers), and her child body and nature reduce her concentration, and readily side-track her.
However, she is very serious in wanting to be a good teacher, making children behave properly, and also in wanting to marry Soün - even though his daughters made it very clear they don't want a new mother, she is still persistent, though she does have trouble not being able to be an adult all the time.
Akari Unryü
Except for his temper, Akari's personality is quite similar to Ryöga's - she's polite, and quite shy (as well as pretty cute), a bit dim, and to her Ryöga is the only man in the world for her. She is willing to wait for as long as it takes for Ryöga, and will forgive him anything.
Konatsu
Because he was brought up as a girl, he doesn't have a typical male personality, and generally acts like and prefers to be a girl. He is rather obedient, and was particularly weak willed in going against his old family's wishes, and is also very much used to extreme hardship. He is very grateful to Ukyö and Ranma (and is very respectful to them) for helping him.
Why doesn't Ranma dump Akane and marry someone else?
The short answer is that he loves Akane, and also, Rumiko Takahashi has stated that they will marry.
Possible reasons why he won't marry specific people: Nabiki (was temporarily engaged to her once, and really didn't like it, and stated he prefered being Akane's fiancée), Kasumi (perhaps wouldn't want to marry woman 3 years his senior, and he might find her a little dull), Kodachi (he doesn't like her personality, or her behaviour), Shampoo (too violent, and doesn't like her methods - particularlly her trying to kill Akane), Ukyö (he sees her more as a friend), Hinako (another older woman, and he regards her as a bit silly, and doesn't respect her that much) and Akari (she's obsessed with pigs and Ryöga).
This was taken from the Ranma 1/2 FAQ website http://www.wot-club.org.uk/RanmaFAQ/. I take no credit because I'm too lazy to write this kind of stuff. I merely fixed some errors. Please visit their site. Preferably within this year.