She is kind of irritating. However, I would argue that she symbolizes- or satirizes- a typical Victorian girl. She is caught between the fantasy and the reality of her situation.
This is an interesting question as the character of Fanny does seem to divide readers somewhat. Her status as a dependent does certainly repress her character, but at the same time, as #3 points out, her refusal to marry Henry shows her indepdence and her gutsy status as an Austen heroine. She is a character who knows what she wants and doesn't want, and will not settle for second best.
I would say that she is, at heart, a free spirit. Her upbringing in her aunt and uncle's house has dampened that spirit a bit. She feels like she has to hold back her own thoughts and opinions. She thinks and feels much that she never says. Fanny's refusal to marry Henry Crawford proves that she isn't a tedious bore. If she were, she would have married him and become the center of fashionable society. Fanny could care less about fashion; she wants a quiet life, but that doesn't make her boring. She can see right through his pretenses and knows that they would be miserable together. Fanny may try to comply with others wishes, but her unwillingness to change her base character proves she is independent at heart.