These are my thoughts on the traits:
Religious is the best. Cheap temples are great for border expansions and getting a start on culture. Culture from temples doubles in very few turns if you build them early enough. They're so easy to build, it only takes 10 shields and a pop rush for a religious temple. The happiness is nice, too. Cheap cathedrals are good, too. You get a lot of happiness for very few shields, especially if you build Sistene (which I always try to do if I'm religious). And the shortened anarchy basically gives your whole civ free turns it wouldn't have otherwise. It allows you to switch to the appropriate government whenever you want, like Despotism -> Monarchy -> Republic -> Democracy. If I'm not a religois civ, I ususally go Despotism -> Republic and stay there because changing to the other governments isn't worth the turns of anarchy.
Industrious is right behind Religious. Both of these traits are helpful in any strategy and are helpful throughout the game. Doubling the speed of your workers has very obvious benefits, especially because one of the units you start the game with is a worker. Because their workers are twice as good, on turn zero, an industrius civ is 50% stronger then any other civ. The bonus shields for cities and metropolises are nice, but not a big deal.
Militaristic and Scientific are nice traits if they fit your strategy, but they aren't useful all the time the way industrius and religious are. Militaristic is good if you fight a lot. Easier promotions give you better fighters and a better chance at a great leaders, but only if you are fighting. The cheaper buildings aren't very important because barracks are pretty cheap anyway, and there's not much reason to build walls or coastal fortresses at all. Harbors are nice, though.
Scientific is good mainly if you're going to do your own research. In other words, it's not that great on deity. Scientific gives you a cheap culture building like religious, but libraries come later than temples, so they don't have the variety of uses that cheap temples do (border expansion, very early culture double). You don't get any benefit at all from scientific until near the end of the ancient era when you get literature, and that's the most critical part of the game. The free techs at each era are cool, especially if you can turn them into good trade opportunities.
Commercial is a not a very good trait because it has a very slow start. The extra trade doesn't kick in until you have cites and metropolises, and even then it is a rather small 2 or 3 trade per city. The reduced corruption doesn't really help until you have many cities in a large empire. The thing is, if you have a large number of big cities, you're already in a winning position, and the commercial trait won't really make a difference whether you win or lose. And while you were on your way to the winning position (when the cities were small and few) commercial didn't help much at all. Yeah, having a large, efficient empire is fun, but I don't think commercial really helps win games.
Expansionist can only compete with the other traits on a big pangea map, and even then, its benefits depend on the luck of the huts. Techs and settlers are nice, but on harder difficulties, you're much more likely to get gold, warriors, maps, or nothing. Exploring with scouts will help you get more contacts and a better map than other civs, and if you're carefull with diplomacy, these can be traded effectively. But still, it's all over in the ancient age, and expansionistic doesn't help at all after that.