Each civilization has two traits (except in scenarios, where this is usually but not always true). In the epic game, the civs have been carefully designed so that every possible combination of traits is held by at least one civ.
It is not possible to say what the best or worst traits to have are, because everybody is different. Some people may even like "weak" traits because they make the game interesting, or they feel they can really use the advantages the trait does offer. There is also no consensus: some experts feel that Commercial is weakest, while others feel it is the strongest! Therefore, what traits are desirable to you must be decided yourself.
Commercial
If you are constantly spending money to rush-build, and maybe you need to research just a tiny bit faster, this trait may be just what you need. While you will experience less corruption throughout the game, the real effects of the trait will not be pronounced until the middle-game, when you also have cities beyond size 6, which will have one extra commerce per turn. Your advantages will be most pronounced at the end-game, where such considerations are very often relevant.
Expansionist
In contrast to the Commercial trait, the Expansionist trait has its strongest benefits early in the game and virtually no benefits by the end-game. That means your advantage will not last and it is vital that it be played correctly, lest you waste one of your two traits. All civilizations need to be aggressive in the early game, and that goes double for you.
You begin with a Scout unit (and the ability to build more), whose two-tile movement rate is a huge boon for the first few turns and helpful for many more. These scouts will likely stumble upon a good number of goodie huts, leading to your other advantage: you will never encounter goodie huts with barbarians. Not only do you not have to treat every goodie hut as though it were "loaded", but that means that the more desirable results, such as a new Settler or city, or a free tech, are more likely.
Industrious
The benefits of this trait will last you the entire game. Your workers (except enslaved workers) will work faster. You also build things faster: you get a free shield per turn in every city. Of course, you won't have as many shields knocked off as you would for, say, a temple if you were Religious. (If you're Scientific or Religious and Industrious, then you can really build!)
Militaristic
Buildings like barracks are cheaper, but you've got to build them to take advantage of them. Unit promotions occur more easily.
Religious
If you want to wage a culture war, you definitely want this. This gives you temples and other religious structures at half price, effectively meaning they will be constructed twice as fast and they can be rush-built sooner. It also effectively makes your citizens happier if you, as you should, build Temples and Cathedrals sooner than you normally would. Also, it only takes one turn to change governments.
Scientific
A scientific civilization receives a free civilization advance when the civilization enters a new age, provided there exists an advance in the new age. The civilization advance that is received is the cheapest available tech, that is, the tech costing the least amount of scientific research. Buildings marked as scientific also cost half as many shields. In Conquests, a scientific civilization has a 5% chance of spawning Scientific Great Leaders when they are the first civilization to discover a new tech, as opposed to the 3% chance for non-scientific civilizations.
The scientific trait is generally useful with another trait that also gives cheaper buildings (Militaristic or Religious). Thus, in the epic game, Babylon (scientific and religious) and Germany (scientific and militaristic) are often good choices for players that wish to exploit as much of the trait as possible. In particular, Babylon is an ideal civilization for culture wars.
Agricultural
Cities will have +1 food. However, in Despotism this only occurs on cities sited directly on rivers. Therefore, agricultural civilizations highly value rivers and will invariably build on them when possible. This can be used by rival civilizations to predict expansion — it is usually wise to build on rivers anyway, but they will have much higher priority for agricultural civs.
Seafaring
Your civilization is more likely to start near the coast of an island or continent. The capital also has a commerce bonus, which will likely keep you on par or better against the AI even on higher difficulty settings below Demigod.