Not entirely sure which is my favourite, I like them all equally for different reasons, though would admit there are some that have weaknesses.
Human Noble - Probably one of if not the shortest and yet sweetest, ok it ain't sweet it darn right reeks of "I wanna kill howe NOW!", but you can never fully appreciate the sweet until you've tasted the sour and so have to go through that sour spot you can get your sweet vengeance later. Part of me still thinks it could have done with a bit more to it.
Mage - Probably second shortest (although possibly only just pipping female city elf) and as at least one other person has mentioned it ends up being more of a 'Jowan' Origin with player tacked on the side. Especially if you don't tell Irving about Jowan's plan. Can someone tell me if playing a female mage when you meet Cullen in the tower later on and you were flirty with him in the origin if there is any followup?
Dwarf Noble - As others have said, solid and gives us an insight into Dwarven politics in Orzammar. Only done the origin with a male so far but was best buddies with Gorim and yes I've met him in Denerim, shame he can't become a party member
Dwarf Commoner - Have to say if I really had to, this would probably rank as my favourite. Again brings insight in the Carta and the caste system. Thing I liked about the origin encapsulating the whole story was coming back to Orzammar and for a 2nd time becoming champion at the Provings. As someone else stated, Duncan's comment about the commoner being the Champion really did speak volumes.
Dalish Elf - Really not sure what to think on this one, there is a fair bit I like about it, but it just seemed a bit rushed to me. Also whilst I know of a certain situation that happens through the story, I was wondering if anyone turns up from the Dalish Elfs original clan at the end (or their dad even, seeing as he is mentioned a lot but you never see him).
City Elf - Whilst it probably is a tiny bit shorter, got to agree with others that the "Damsel-in-distress" rescuing herself and her friends really is a good spin on the old tale and like the other origins gives a nice insight to how the city elves are treated.