When I was finally able to fly back to the US from Canada on Sept. 15 I was asked for 2 forms of ID. I don't know if this is standard for Canada-US travel, but I didn't need two pieces on the way there (before Sept. 11). And I don't recall needing two pieces on my European trips. (And on previous car trips to Canada and back, my DL was enough.) Fortunately, I now always travel with my Passport and DL.
So, depending on the airport/airline it's possible that you will have to have not just one, but two pieces.
If you don't already have one, I recommend getting a Passport. It seems to be universally accepted. State licenses can vary; most look pretty official now, but in the past I remember seeing some that looked pretty amateurish. Visiting bars with fellow students produced a variety of licenses and occasionally a bartender/waiter seemed rather dubious of some.
If you move as frequently as I do, you don't have to worry about having inaccurate/conflicting address information. And if you keep your passport with travel accessories, you are less likely to lose it.