1. "Break" by yahtzee63. Part 1 | Part 2 | Part 3. This was the first fic I ever read in ST fandom and I was blown away. It's the author's take on how Spock & Uhura get together, with a decent helping of Kirk and some nice touches with Gaila. Rated R, whole fic ~ 26,000 words. Spoilers for the flick.
2. "Of Two Worlds" by yahtzee63. Part 1 | Part 2. So, pretty much anything by yahtzee63 is amazing. This is a Spock-centric story about Spock having to choose between the Prime 'verse and the reboot 'verse. It comes with a generous helping of Spock/Uhura and an interesting mix of a character from other Trek 'verses. Rated PG, unknown word count.
3. "Lunch and Other Obscenities" by rheanna27. Uhura-centric about her relationship with Gaila. Funny and heartwarming, and it also comes with a side of Spock/Uhura. The summary reads: Nyota liked her roommate just fine until she met her. Rated PG-13, ~10,000 words.
4. How Many Roads? or, 27 Times Jim Kirk Hit On Nyota Uhura by captanddeastar. Mostly a Kirk/Uhura friendship fic with underlying Spock/Uhura. It covers from their first meeting through to their last, and it's hilarious, heartwarming and tearjerking. Rated R, ~9,000 words.