Don't spoil anything.  I played through one of the origins stories (just the beginning I haven't finished the game yet) as a Darish Elf Rogue and it was alright.  Nothing spectacular.

I have only played through 3. I found the Mage one to be okay, the Human Noble to be pretty boring but the Dwarf Noble was a really enjoyable one. 
 
The Dwarf Noble though was my first playthrough so that also helped my impressions but I just found the story to be pretty interesting as well as the ins and outs of dwarven culture.

I've played through two - first time with Human Noble, second with City Elf. City Elf was way more dramatic, but Human Noble set up the story better.

Dwarf Commoner.
 
YOU GET TO BE A GLADIATOR DUDE!

City Elf, followed by Dalish Elf.

I liked the dwarf commoner origin the best

Dwarf Noble was actually the only interesting part of the whole game to me. The rest of the story was so, so unoriginal and bland. The only thing that kept me going in that game were the characters.

Dwarf Commoner or Noble, I hear, is good.

City Elf as a lady. Feels good to murder those human scum.

Dwarf Noble is awesome storywise, as it takes twists and turns. It's full of political intrigue.

I played them all, and the only origins I didn't enjoy were the elf ones. The others are longer and seem to set up the story better.

I played a Human noble and mage (elf)
storywise i think the human one is kinda lame, you cant kinda tell

I played Human Noble as female. It was pretty fun.

I'd go with Dwarf Noble. You get to be a prince / princess, lots of political intrigue that ties into the main quest later on (much more so than other origins) and if you want, you get to steal a lot of glory and become a gladiator. It's definitely the most involved of the Origin stories. 
 
Oh yeah, they also toss in a love story for good measure, too.

I thought the City Elf origin story was pretty cool. It starts off rather slow, but it's total Braveheart. I also liked the Mage story, probably more so because it meshed well with the Erl of Redcliffe quest line.

Dwarf Commoner was the funnest and awesomest for me, human noble was OK, but i hated that you only got one choice. also Dwarf noble was kind of cool but not as much as commoner, and the elf ones felt too boring and easy, especially city elf, compare the stuff you have to do as human noble to city elf and you'll find city elf is super easy.

My first playthrough was as dwarf noble and I thought it was great.  The provings are pretty cool (and easy, but that wasn't really a bad thing).  Indeed though, I was very eager to get back to Orzammar and see how I was received and

I haven't played either of the elf ones, but out of the other 4, easily the dwarf noble.

I thought they were all pretty spectacular, except for the Dalish elf one which I found kinda blah. 
 
Personally, I enjoyed the Dwarf Noble origin and being a royal prick to anyone who approached me... plus... your dwarf companion (the name escapes at the moment - Gorin, I think...) is pretty cool.

" Dwarf Commoner.  YOU GET TO BE A GLADIATOR DUDE! "

I've done them all (and not really much else - but I digress) I think they go in the following order:
City Elf  - most catalyzing events
Mage - since magic is 'hot' issue in the game it's interesting to get more of the mage perspective
Dwarf Noble - great side kick and decent set up (also crosses over slightly w/ the Commoner story - but you'd have to play it 1st to get the reference)
Dwarf Commoner - pretty straight forward but fun enough (see above - maybe you could make the connection playing this second - but you'd have to remember some names)
Human Noble - predictable but solid - no major complaints but nothing to praise either
Dalish Elf - BORING. That is all.

i liked the city elf origin the most.