If you hover over the crew in your cargo, it should give you a breakdown of the bonuses each level grants. Aside from the stat boosts, the major difference in crew level is an improved ability to lead targets (aiming where it will be instead of where it is).
It's always good to have high-level crew in ships that use ballistic weapons, since the bonus to aim matters so much with slow-travelling projectiles. Other than that, it depends on your personal play style. If you travel with a carrier fleet, Elite fighters are much more likely to survive, but unless you're very good you'll go through crew faster than new ones level up. I personally like to have my frigates elite, fighters veteran, and everything else uses what's left.
As an aside, Green crew are almost never worth it unless you're severely low on cash, as they grant penalties to your ship instead of bonuses (see below for the sole exception).
Also, keep in mind that the percentage of crew that needs to be experienced goes down as size category increases, so Veteran and Elite capital ships are a possibility. You can then fill the remainder with cheap Green crew.
Edit: ninja'd. I need to stop taking so long writing these things.
