Can you be arrested for a worthless check written over twenty years ago?

If you wrote a worthless check to defraud another person or entity and that person was actually defrauded, then you could be arrested. Your state will have a statute of limitations (i.e., a number of years after which you cannot be charged with the crime). Twenty years seems like enough, unless there was relevant recent activity in connection with the check.

Added: Insofar as private collection activity is concerned, there is little or no SOL's on the efforts of creditors to collect on the bad check. At the very least it could certainly wind up being a 'ding' on your credit rating.