It also depends on whether you're a US grad or an IMG, the rules tend to be different.
All states will require some paperwork from your residency program, usually documenting the length of training and whether your work was satisfactory. It will also depend on whether you quit, or were fired. If you were fired for cause, then the residency program will likely be required to report that to the state licensing authority. That doesn't mean that you won't get licensed, but it certainly means there would be more scrutiny.
Since no one has linked to it yet, here is the list of all of the states and their basic licensing requirements:
http://www.fsmb.org/usmle_eliinitial.html
You should check the specific link (on that list) to the state you're interested in.