People just never appreciate the better things in life...or the better characters. Ukyou is one such character - forever in the shadow of Akane, lumped into the same category as all of Ranma's other unneeded and unwanted fiancees, and criticized for her idiosyncrasies and unorthodox actions.
Kuonji Ukyou was betrothed to Ranma at the tender age of six, and a dowry was set - the family okonomiyaki yatai, or cart, no less. True to form, Genma stole the cart and Ranma from young Ukyou's life, leaving her bereft of her friend and her inheritance.
Little is really known about Ukyou's progress from child to young woman, but she meets with Ranma a decade later in the guise of a man. How ironically appropriate. In any case, after all was said and done, Ukyou's true gender was revealed to the hitherto-unsuspecting Ranma.
It turns out that Ranma hadn't even KNOWN that Ukyou had been a girl. Well, tell THAT to Akane and her avenging mallet.
Ukyou had set up a restaurant in Nerima called 'The Ucchan's', which incidentally leads in to Ukyo and Ranma's nicknames for one another. Ukyou calls Ranma 'Ranchan', short for Ranma-chan (not to be confused with the 'Ranma-chan' associated with female Ranma), and likewise Ranma calls Ukyou 'Ucchan, short for Ukyou-chan. The suffix 'chan' in Japan is a term of familiarity, used among peers.
Regarding Ukyou's relationship with Ranma. Where Ranma actively tries to keep Shampoo or Kodachi at arm's length when it comes to relationships, it is quite different with Ukyo. He's friends with her, and he talks to her as he would a friend, and Ukyou reciprocates the relationship.
However if Ukyou tries to further the relationship (and she has done this very rarely) Ranma becomes panicked. Where he would *normally* reject Shampoo's or Kodachi's advances outright (since he is quite used to them) he tries very hard not to hurt Ukyou's feelings, and since he doesn't know how NOT to hurt her feelings while dealing with her in these matters, he becomes very flustered.
Bottom line, he doesn't know how to react when Ukyou makes a pass at him, and Akane doesn't help any considering her legendary jealousy.
Speaking of Akane, Ukyou's relationship with her is a bit weird. On the one hand they seem to act like friends; having tea together, having a meal together, visiting her at the Ucchan's with Ranma, Akane taking care of her when she was sick. But on the other hand, Ukyou often goes to great lengths (not nearly as drastic as Shampoo or Kodachi, mind you) to get Ranma without considering Akane or her feelings at all.
All in all, Ukyou is one of the more interesting characters even though she doesn't appear nearly as often as Shampoo or Kodachi do, even if she doesn't try as hard as the two aforementioned 'fiancees' to get Ranma. She is a character who needs to be looked into with more detail, with more objectivity than usual in order to fully appreciate who she really is.