"I am sorry for Miss Crawford; but I am more sorry to see you drawn in to do what you had resolved against." ~Fanny Price, Mansfield Park
Fanny Price makes me think of Amy Dorrit. Sweet, quiet, and sensible, she cares deeply about her family and friends, and she has high ideals and principles. The best word to describe her would probably be "retiring". Or maybe "timid". Or perhaps even "painfully shy". (Yes, I know that's two words, but sometimes I need a modifying adverb.)
Fanny has been harshly criticized by many Austen readers, and that's a real shame. She's timid and mouselike, and at first glance she doesn't appear to have much backbone. She lets her pretentious relations walk all over her. The Bertram family was kind to take her in and lighten the load on her mother--and yes, she should be grateful--but that doesn't give them any reason to treat her like a servant and constantly remind her that she is not of the same station as they. And Fanny puts up with it without a complaint. Her meekness is admirable, but at the same time I can see why some people think she's a doormat.
When the Tom Bertram and his sisters, along with the Crawfords and Mr. Rushworth, decide to put on a play and invite the neighbors to watch, Fanny steadfastly refuses to take part, because she knows that Sir Thomas Bertram wouldn't approve. (In those days, playacting was frowned upon, as many plays were bawdy and inappropriate, especially for high-class society.) They tease and pester her, but she sticks to her guns. Edmund Bertram at first protests too, but then he finally gives in and plays the part of Anhalt; if he didn't, his sisters would invite other friends to join in and he couldn't bear to have the whole neighborhood drawn into the brouhaha. Fanny is disappointed that Edmund didn't remain firm, yet she is understanding and forgiving.
Fanny also displays strength when she refuses Henry Crawford's proposal. Most girls of her station in life would have been thrilled by a proposal from a young man of large fortune (I wonder if he has FIVE THOUSAND a year?), but Fanny didn't let that sweep her off her feet. She knew that Henry Crawford wasn't her ideal husband--in fact, that he wasn't anybody's ideal husband. He didn't measure up to her standards of morality and character, and therefore she took a deep breath and refused him. And she held her ground when Sir Thomas tried to convince her of the folly of her decision. She knew that Henry wasn't to be trusted... and she was right. Plus, she was already in love with Edmund (even if he didn't know it) so why would she want to marry Henry?

And... he doesn't realize that he's in love with Fanny until the second-to-last page in the book. Although that was Jane Austen's fault. (Don't kill me, Miss Laurie and Melody.) "... And not a week later, Edmund did cease to care about Mary Crawford, and became as anxious to marry Fanny, as Fanny herself could desire." Talk about hastily tying up loose ends! That sentence was quite a let-down for me. I wasn't expecting a mushy-gushy proposal (this is Jane Austen, after all) but I was at least expecting something along the lines of, "Fanny, will you marry me?" You know, simple question, no frills about it, but actually getting the point across.
However, there is a redeeming quality in the whole Fanny-and-Edmund thing: they are, in short, Fanny and Edmund. Just like another couple "of which I know of".. except, of course, that these two are not at all like the illustrious Mr. and Mrs. Sparkler (who have no nonsense about them). [I'll take this opportunity to point out that Anne-girl and I read/saw Little Dorrit before we discovered Mansfield Park, and were most excessively diverted by the coincidence of names.]
In conclusion, I like Fanny Price because I respect her. She's not quite perfect, but, then again, if she were, I probably wouldn't like her anyway. Perfect people are... well, boring. (Apologies to any and all perfect people out there.)