Forst thing's first, some civs are better for an objective than others.
So while some civs are very good at war, some genrate culture better, some gain techs faster, thusly not each civ is made for, say, a diplo vic(it'S doable, but i highly doubt that the mongols would be good at this).
For waging war, i really like the aztecs. they expand fast because of agricultural trait
(half-priced granaries), have a great UU for scouting and getting goodie huts(although you aen't always likely to get some good out of them) and the militiristic trait is a plus.
For cultural, Babylon, Sumeria, and(oddly enough) celts generate very good culture
As for Diplo and Space race, i like the greeks/koreans and Persians/Ottomans. I think these are the 4 civs who generate the msot scientist.
Those are my 2 cents, and it's my opinion.