Angel Baby1 ~ Atlas, available at
http://www.fanfiction.net/s/5344838/1/Atlas Atlas ~ Nu!Trek Kirk/Spock - a study in the evolution of acquaintances into friendship into t'hy'la. If you read only one Kirk/Spock fic on this list, this should be it. Also, really, anything that Angel Baby1 has written is very much in the to-read list.
Anrui Ukimi ~ Western Skies, available at
http://www.fanfiction.net/s/5485844/1/Western_Skies Western Skies ~ Semi-fusion with X-Men, but in such a way that absolutely no knowledge of that canon is required at all. Otherwise known as the one where Pike raises Jimmy and does a pretty damn awesome job. Gradually becoming Kirk/McCoy, but we're approaching 200k and have barely got to that part, so don't let that put you off.
Ceres Libera ~ Switch, available at
http://ceres-libera.livejournal.com/679.html Switch ~ Nu!Trek Kirk/McCoy. Briefly summarized by the author as the life and times of Leonard H. McCoy, M.D. Otherwise summarized as how two men go from "I might throw up on you." to forever. If you read only one Kirk/McCoy fic on this list, this should be it.
Keira Marcos ~ Tangled Destinies, available at
http://keiramarcos.com/star-trek/tangled-destinies-ks/ Tangled Destinies ~ Well, this is a borderline ridiculously AU fic in which Spock and Kirk meet while children. But it's well-written and makes me smile, so who cares? Nu!Trek(ish), Kirk/Spock
Kyliselle ~ How High the Moon, available at
http://kyliselle.livejournal.com/4014.html How High the Moon is one of those stories that just will rip your heart out and stomp all over it. Basically, Kyliselle decided to do a story in which soulbonding kind of sucks. Good fic for when you want a good cry. Nu!Trek, Kirk/Spock.
Waldorph ~ Illogical (√π233/hy7), available at
http://archiveofourown.org/series/635 Illogical ~ The one where Kirk ignores Pike's dare (nu!Trek, obviously) and instead becomes a bartender in San Francisco. Which would work, really, except that he has an unfortunate tendency toward solving Professor Spock's problems on boards at Star Fleet Academy. Kirk/Spock.
Mijan, archiving at
http://mijan.livejournal.com/195083.html#cutid1 Oh gosh. Mijan could write Hi! on a biscuit with frosting and I'd probably still want to read it. He's got some gorgeous prose going on over there - just really well-written (predominantly Kirk/McCoy) fics. I particularly recommend And All the King's Men, which is an academy era Nu!Trek pre-Kirk/McCoy fic that's really just eight different kinds of awesome. And it has sequels. Mijan's most famous is probably Redshirt, which is also awesome, and I'm partial to Secret Garden, which I personally find just beautiful.
Honorable Mention:
T'Key'La, archiving at
http://www.fanfiction.net/u/1854335/TKeyla T'Key'La has spotty characterization and tends to leave plot holes that I could drive through, but hir fics are absolutely a guilty pleasure of mine. Good for when you're feeling self-indulgent or looking for a Kirk/Spock fix. I recommend Kirk, James T. Kirk and Epiphany particularly.
Alternative Resources:
Shadowloverk's Tarsus Fic Rec List, archived at
http://shadowloverk.livejournal.com/4521.html#cutid1 Shadowloverk basically did all of angst, h/c lovers of the world a favor and collected every fic referencing Tarsus which is just a giant source of angst. Some of the fics are awful, some of them are brilliant, and the list is only current through July 2010. Still, good in a pinch.