Television:
Chloe O'Brian from 24. She's abrasive, painfully blunt, sarcastic and terrible in social situations but still manages to be completely endearing.
Tara from BtVS. I can't believe I've just picked her over Willow, but I love her character so, so much. She's introduced as awkward, stuttery and painfully shy, but the viewers and the rest of the cast get to see her grow and change into someone more confident as she overcomes her personal demons with the help of her friends. She's the nicest, most selfless person on the show, but is strong enough to know when a relationship turns abusive and gets out; she's quiet and soft-spoken, but she sometimes knows the other characters better than they know themselves.
Honourable mentions: Moss from The IT Crowd, Edgar from 24, Olivia from Law and Order:SVU, House from House, Karen from Will & Grace, Liz from 30 Rock, Everyone in Pushing Daisies, Jaye from Wonderfalls, Veronica from Veronica Mars, Willow from Buffy and Chandler from Friends.
Video Games:
Raine Sage from ToS. I think what I love most about Raine is how many different sides we get to see of her - teacher, sister, parent-figure, healer, scholar, daughter, victim, friend; and in addition to all the roles she plays, she's a walking contradiction; she's a White Mage who kicks at least four people in the face during the game; she's by far the most intelligent person in the game, but can't cook to save her life; she's the emotional pillar the younger characters look up to, but she's absolutely terrified of water, goes nuts at the sight of ruins and we see her break down in tears twice (once after being abused by the mayor, once after confronting her mother).
Honourable mentions: Every main character from the AA series, most other ToS characters, Etna from Disgaea, Vivi from FFIX, Pikachu from Pokemon and Snake from MGS.
Theatre:
G(a)linda from Wicked. Actually, this is more bookverse than musicalverse, but still. I love so much how we get to see her change from an empty-headed bimbo to someone who wants so much to do the right thing - she's not perfect and isn't strong enough, but we get to see her learn and change and grow and eventually realise that the wrong choices she's made will make her desperately unhappy - in many ways, I think she's much more tragic than Elphaba (who I also adore).
Angel from RENT. In a cast of amazing characters, it's so, so hard to pick my favourite, but I think it has to be Angel. She's such a beautiful person; she doesn't take being alive for granted for a single second, and just her presence can light up a room - even one as sad as a Life Support meeting. She's the emotional glue holding the group together ("Angel helped up belive in love"); and her self-confidence is just beyond amazing <3
Honourable mentions: Everyone else in RENT, Jean Valjean from Les Mis, Rod and Christmas Eve from Avenue Q and Ryan from HSM.
Anime/Manga:
If I start talking about how much I adore Yotsuba, I'll never stop. Suffice to say I think she's absolutely, totally and utterly fantastic in every possible way.
...I also love the Azumanga Daioh cast. Yeah, yeah; Azuma fangirl.
I'm sure I've forgotten some, but those are the ones that jump to mind :)