Originally Posted by braumeister
Every state is different in how avidly they will pursue you for taxes, but voting in federal elections is easy. This site will help:
I concur with braumeister, a correct (but not only) method is to use the FVAP site.
Voting is normally where your last US address was situated. Providing ballots to overseas voters is supposedly mandatory, although there are reports that some States are not as easy as others.
Taxation varies. Check to website of your last State's tax administrators for the treatment of "residents abroad". Many use the federal exclusions, some have different exclusions, and one or two don't know what abroad means. Most States have a time limit (12 to 18 months) after which you are non-resident for tax purposes.
The stickiest States seem to be California and Virginia. To no longer fall under their jurisdiction, everything from drivers license to library cards must be done away with. Even they have to give up eventually if you follow their rules.
If you have income generated (sourced) within a State, you'll need to check the State tax authority to find your responsibility. If you do not want to file a State return, at least find what risks are associated with that decision.
Personally, I never had a problem in over 30 years. Voted, and that was it. I never heard a word from the State tax people.