In order of preference:
1) Human Noble - It is the only origin in which Highever is actually visited, despite being mentioned throughout the game. It gives a reason for us to care what happens to Arl Howe and context as to why he is present at so many of Loghain's interactions. It gives crucial significance to Nathanial's character in Awakenings. If one is so leaning, it also provides the player the opportunity to ascend to power.
2) City Elf - This the only origin where my character truly wanted to become a Warden. Regardless of which gender you play, this is a horrific origin and becoming a Warden is a welcome escape from a scenario that otherwise would have been terribly messy. It also makes the Alienage story near the end of the game a much better affair than it is otherwise.
3) Dalish Elf - I don't particularly like the Dalish, but my feelings on this have changed in the time since I originally played it. It introduces the Eluvians, does a good job of making the loss of one's clan feel heartbreaking, and it helps make the Brecialian Forest section slightly more interesting. You get additional interaction with Velanna in Awakenings and it provides immeasurable context for the Dalish in Dragon Age 2.
4) Mage - This used to be my third favorite. The return to the Tower becomes a nightmare since you are familiar with most of the people involved. It gives some additional interaction with Cullen, which depending on how you feel about him might be a positive. I was never bothered by Jowan's role in this - I think it helps towards understanding his role in the Arl of Redcliffe chapter and he never got on my nerves. It also gives some additional meaning to your interactions with Morrigan and Wynne, and ties you slightly to Hawke in Dragon Age 2.
5) Dwarf Commoner - Almost as pressing as City Elf, but then it just fell flat. The unfortunate truth is that it didn't move me, and thus I found it hard to care.
6) Dwarf Noble - Regardless of the politics, regardless of the context it gives during the Orzammar chapter, regardless of everything that should make this enjoyable, I despised it. The whole thing is a railroad job; at no point after speaking with Bhelan would I have simply just ignored everything until the next day. I would have found Triann and we would have had words - and something different would have happened. I was furious when the game didn't give me that option, and even more furious when the remaining events played out as they did. It's the only origin where I never completed Ostagar. Deleted the character and started over with a different origin.