Fun, isn't it? I remember my first time on singletrack. I was maybe 10 years old. The term didn't exist then. It was pre-mountain-bike, and I had found this trail in my neighborhood that went, well, who knew where it led, right? So I begged my mom for permission to find out.
Cyclocross bikes are pretty capable. You could ride most or even all of what's near me on such a bike.