Back in the 80s I lived in Berlin and worked as a contractor for the US Military. Because Berlin was an "Occupied City" at the time and I had US plates on my car the Berlin Police had no jurisdiction over me and could not give me a traffic ticket. Prior to moving, I sold my car and drove a rental car for a month (with German plates). Back in the states a few months later, I received three speeding tickets in the mail from the car rental company (photo radar in Berlin). I never paid these tickets. This was over 20 years ago. Does Germany have any kind of statute of limitations on tickets? I travel to Germany quite a bit and don't want to get pulled over by the police for a ticket and find out there's a warrant out for my arrest.

First of all: dont worry. nothing can and will happen.

It depends on what the authorities did back then. The maximum amount of time they could go after you would have been five years, that is if they filed a "Bussgeldbescheid" for a very high amount.
There is no warrants for arrest for unpaid speeding tickets, unless this would have been a special case but then we would have heard in the news...

Danks