Passengers are routinely screened by TSA's Secure Flight database. This database requires certain identifying information and then matches it against certain government databases. If there is a match you may find yourself on a No Fly list. The hitch is that you will only know whether you're on the list when you are denied boarding.
NOTE: If you have a ticket purchased online you can usually download your boarding pass 24 hours in advance of your flight. If you are able to do so you are NOT on the No Fly List.
Will State Traffic or Misdemeanor Warrants Keep Me From Flying?
I'm not promising anything these days but they shouldn't. Most states don't match their data with TSA's. The TSA checks data maintained by the FBI and Homeland Security. It is highly unlikely you'll find a state warrant on either one, murder, arson, rape and kidnapping excepted.
Then What Happened to Roman Polanski?
The famous film director was arresting getting off a plane in Switzerland from France. He was not arrested because the airline ran a warrant check but because he is a high profile target and the US government,knowing he was going to be in Switzerland, filed an international arrest warrant with that county's police. It is highly unlikely you would be the object of such scrutiny.