May as well voice my opinion while I wait for a game to fill.. I think it depends on your play style as to which civ you will play best with,
IMO:
1) French
By far the best civ in my opinion. Excellent economy, european benefits (Factories and cannons). Walls (a luxury greatly underappreciated) *cough Sioux players*. Your colonial age rush is pretty simple, usually muskets or cav. Your eco can happily support either since your villagers are superior. Everybody hates you late game, superb eco and well, cuir spam. And I mean spam. Instant cuirs with an economy that can support it long term. Everybody fears you and considers them OP. Ive been in many games where people have quit once the french made IV.
2) Japan
Not as good as French IMO, ok the eco is good and the army is strong. But. You are limited with your cannons, think everyone would falconet > flaming arrow and your army build speed cannot reach instant. Still, easy to play, no worries about being raided early game since you stick the villis quite happily on the cherry groves, shrines practically throw resources at you, and your army will put up a decent fight! Again, considered OP by many.
3) Personal favourite: China
Ok underpowered like Russia many people say.. But I don't think so. Nothing special regarding economy although Ive stood up to many european civs with no resource problems.Little underpowered at colonial but *still learning* make a decent rush strategy and you'll be fine. Age III and above, you're laughing. Army strength improoves considerably, you can hold your own and age IV? Infinite flying crows and you're done. Backed up with skirms and anti cav armies, when Ive gotten to this point in the game, I;ve yet to be beaten. Ok Im a MS but it's a strong combination to defeat, definatly worth trying! Easy civ to use and not considered OP by anyone :P
Other
Sioux - Favourite Civ (more so than china) Strong army, but weak economy late game to the point you cannot hold your own. No walls mean if your allies do not wall you in properly, you're buggered. Excellent rush and considered OP by some, but really no need as they have their weaknesses.
Russia - Euro economy, instant army, although weak. Powerful contender throughout the game, and if the game begins to skew, just roll out the opri's.
German and Dutch - Both iffy IMO although many use these well early game. Skirm hit and run and Uhlan raiding are their best strategies that Ive seen. Late game, very powerful and Dutch villagers are limited to 50 because of the banks so useful for a large army.
Brits & Iro - Starting to group civs now coz this is where I find them boring. LB spam or rapid rush with Iro. Both decent economies, Brit with the added bonus of houses = Villager. Not very varied units beyond that and not a huge fan of either civ.
India - Pleasently suprised by these recently. Little tricky to play if you consider villagers cost wood, but easy to reserve all your food to age quickly. Armies strong, fort gives the edge during colonial,and eco is decent. Still, found them a little boring.
Spain, Ottoman, Portugal and Aztecs - Boring. And Aztecs have no horse units.. Bugger them. (Coyote dont count.. do they have 4 legs? no.)