I had a complete hysterectomy in 1999. My question is do I need any more pap tests?

Depends if they took out the cervix or not. Usually they do and tie off the end of the vagina canal. If the cervix is still present than it can still become cancerous, even with nothing behind it. This is a question for your OB/GYN the next time you see. A quick exam will determine whether you'll need a pap smear.