For men in the United States, from what I've seen, about 1 inch of length up top, about 1/2 on the sides and back, with a fade done so it all blends together. This works well with my curly hair; other possibilities certainly exist.
In general, though, any male haircut that doesn't involve long hair (except as a comb-over) is considered reasonably conservative in the US. Though it might be said that the less it looks like it came from GQ, the better. In this sense, then, conservative is taken as the opposite of rebellious. If you have a non-conservative haircut, you might find clerks following you around when you shop.
I'm not certain what would be a conservative haircut for women, because it seems a wider range of variance is allowed (though really short/shaved/butch is rebellious in this case).