There's a good mixture of both. And many people (myself included) ride both. Around Denver itself, I'm always on the road bike. There's a pretty darn good network of paved trails, and some good roads to ride on as well. Summer weekends I'm almost always out of the city on at least one day hitting some mountain bike trails in the foothills around Boulder, Golden, Evergreen etc.

I've found it a great city for biking - for the less fit, the flat areas of Denver are amazing to ride around. On the other end of the spectrum, the mountain passes will challenge almost anyone.