Updated 10-Aug-2010.
I may be off by a turn or two depending on when victory was triggered. Asterisk/italics indicate teams' predictions for their finish date (except Fifth Element, which was predicted by kcd_swede)
Plastic Ducks: 930AD diplo (T238)
OSS: 1030AD diplo (T248)
*Barley Demons: 1160AD (t261)
Xteam: 1190AD diplo (T264)
Gypsy Kings: 1285AD (T277)
Fifth Element: 1315AD diplo (T283)
Unusual Suspects: 1320AD diplo (T284)
*ChokoMisfits: 1400AD/T300 diplo
Who Dat?: 1485AD diplo (T317)
Phoenix Rising: 1690AD diplo (T358)
*T'dr...: 1600AD culture (T340)
*Maple Sporks: 1690AD culture (T358)
Smurkz: retired
Looks like a close race for the bronze medal. Man, as a Who Dat? player, writing up that list really depressed me
Some notes:
Xteam: UN built on T254, and gifted to Toku. Finished with Communism as last tech. finished on T264 (1190AD), looking strong. Interesting technique of gaining diplo points with Free Religion rather than shared religion. Considering the religious setup in their came, perhaps not surprising!
ChokoMisfits: T290 now and about to complete the UN. Waiting 10 turns for the vote (did they include the SecGen vote as well?). Still some loose ends with spreading Hinduism and getting resources hooked up, but no problems expected. If it's 10 turns then ETA is T300/1400AD.
Fifth Element: Man, these guys discuss a lot

. They're attacking Mehmed for silk and teching Mass Media at the moment. It's T269 right now (1240AD) and they just liberalized Radio. kcd_swede predicted T283 victory in the Unusual Suspects thread.
Maple Sporks: One of the culture victory teams, M.S. is engaged in a Rifling/Cannon war with Mehmed and Isabella to capture Silk. They just settled the small island between Zara and Isabella (it must have had a previous city that was razed). Victory estimate is 30 turns (1690AD)
T'dr...: Religion spread is in hand and culture win is predicted in 30 turns (T340, 1600AD). Do they have all their GP already? Both T'dr and Maple Sporks are eyeing each others' culture graphs
Gypsy Kings: Mass Media came in around T266 (1210AD), victory in 1258AD (T277)
Barley Demons: UN completed in 980AD (T243), and they just captured DevilsGate. They're about to settle a city on/next to furs and presumably have a missionary ready. Predicted victory 1160AD (T261) - looking strong!
Smurkz: Xcalibrator played a turnset with the interesting leadin "You rule! We're doomed". It's 1300AD (T280) and they are having difficulty gathering the required votes. Their friends are Sal, Mehmed, and Izzy and they want to add Zara. UN is due in 7 turns (T287). They threw in the towel (despite still having the chance to crush Who Dat's finish time

)
Unusual Suspects: Win in 1320AD (T284)