If I'm planning on a long trek on my mountain bike, I always carry a tire lever set and at least a rubber patch kit. I've been known to carry an entire inner tube if I'm going to ride off-road trails. I've replaced tires using only one tire lever, but having two makes the job much easier, especially when the tires fit very tightly on the rims.
The best bike tire levers do have a way to clip onto the spokes while the other lever works its way around the rim. It's hard to keep the tension with one hand while prying out the tire with the other.