Is it possible to get STDs in a monogamous relationship?

Q: Is it possible to get STDs in a monogamous relationship?

I had unprotected sex before I met my current partner. I’m the first and the only partner of the person I’m with now. I recently went to a clinic to get myself tested and I have no STDs. If my partner and I just stick with each other (for sexual pleasure), can we still get an STD through unprotected intercourse or through unprotected oral sex?  

The Problem With Virginity Pledges

By Elizabeth Boskey, Ph.D., About.com Guide

Virginity. It seems like such a straightforward concept, but ask any ten people what it means and you'll get ten different answers. Despite this, the importance of virginity is stressed by many groups, and by abstinence only sex education programs. These programs frequently encourage teenagers to maintain their virginity rather than giving them comprehensive information about safer sex.