I always carry a spare tube and a patch kit and operate in much the same way as douglips.
I never use the slime-like products. They seem to work OK for simple punctures, but I’ve seen occasions when they don’t work and they make a huge mess resulting in hours of clean up. I know a guy that had to throw away a perfectly good tire because he couldn’t get all the goo cleaned off. Also, I’ve ridden bikes with this stuff in the tubes and I don’t think they feel right, especially over rocky terrain.
I use have some of the kevlar tire liners, but I don’t even bother to use them anymore because they never seemed to make a significant difference and they’re more trouble than they’re worth on the trail. I prefer a tire with kevlar in the bead. These are more expensive, but they’re more durable and you’ll spend more time on your bike, so it’s woth it to me. (check out the sales at bike nashbar)
Anytime you have a flat, take the tire all the way off the rim and turn it inside out. This can be very difficult sometimes with mountain bike tires. Once it’s inside out, feel carefully in both directions all around the circumference. About 1/4 of the time, the culprit remains in the tire. It can be difficult to find without inverting the tire. Also inspect visually from the outside - sometimes a thorn or piece of glass may be visible.