Ok, I'll bite.
As others have pointed out, it totally depends on your playing style, but for me, the Babylonians win hands down. I'm neither a completely peaceful builder nor a warmonger. I like to build up peacefully and then, once I hit a sort of "critical mass," conquer a few civs and then settle down and build the spaceship. My most dominant games (playing Monarch) have been as the Babs, and several of them could easily have ended as "domination" victories, if only I'd had the patience to keep fighting... which I find gets dull after a while. Once I have access to all 8 luxuries and all the necessary strategic resources I just don't care to fight anymore, but that's me.
Civ traits - Religious/Scientific.
If left alone for a while in decent terrain, the Babylonians are a timebomb. Religious provides cheap temples (and later cathedrals) to get those borders to size 2 quickly, and keep your people happy, not to mention contributing to your overall culture. Additionally, government switching costs you only 1 turn of anarchy, which is a HUGE advantage (I switch twice: despotism-> republic->democracy). That's 2 turns of anarch instead or 10 or so. Scientific provides cheap libraries and universities (which, of course, also provide tons of culture), plus a free tech per age (3 total, then). On its own, it's nice. Put together with religious, it's awesome. The turn advantage you get from 1 turn anarchy, added to a free tech per age and the ease with which you can build your key city improvements just plain ROCKS. You will find you have plenty of time to build up your armed forces... and rest assured they will be top of the line (technologically speaking, of course).
The beauty of the babylonians is that you may never need to fight, but if you do, you will do just as well as a militaristic civ (better, in my opinion), due to the fact that you should have better tech and more units (stronger economy/core cities). Build the right wonders, and you can essentially MAKE yourself militaristic (Sun Tzu + heroic epic). The Babs also excell at cultural war, of course. A rival beat you to a key city site early on? No problem, build your city as close as you can, and rush all the cultural improvements, and watch that rival city become your city.
For a new player, the Babs just make a number of things easier.
This is not to say that other civs aren't any good. Not at all. The Persians are also solid, as are the Egyptians (though beware their usual neighbors, the tough-to-conquer early on Romans and Greeks). Industrious gives you a nice jumpstart on expansion (quick roadbuilding/mining near your core cities) and is really nice once you start building railroads.
The Iroquois have that NASTY Mounted Warrior, and the French, I'm told, have a pretty solid combo of attributes, though I've never played them myself. Again, civ choice depends on your playing style, not to mention the type of world (expansionist civs do better on larger worlds, for instance).
-Arrian