I love riding my cross bike on single track. When I built my first bike frame for myself, I choose to build the Frankencross. The idea was to build a cross frame that was more specific to riding on the rocky single track found on the Front Range in Colorado. The epitome of this is Heil Ranch. This trail has been called the rockiest trail around by the likes of Velonews and is considered a perfect testing ground for big tire, suspension laden mountain bikes. So naturally, I consider this perfect riding for the Frankencross bike.
Riding singletrack on the cross bike teaches you a lot about bike handling. Riding THIS trail on a cross bike teaches you a lot about surviving. Sharp rocks, boulders, steep climbs and descents abound and it is a ton of fun if you have the right equipment and attitude. I hardly ever ride my mountain bike (full suspension Specialized FSR Pro) any more due to the enjoyment derived from a fully rigid steel bike can provide on a tight trail. Although I do enjoy the full on aggression to be found on the full suspension rig, there is something more interesting having to pick your way through the rocks and ride with more skill to avoid popping a tire or eating a tree.
If you are into cross racing, get out on some single track. And don’t be afraid to push the norm. If your just into fun, get out on some single track on a cross bike anyway. (although be careful on these rocky trails, I sliced my tire clean thru in no less than 10 spots)