Always bring water. Especially in the heat, which is even more wicked when you're exerting yourself. For a whole day out, one or two water bottles are not enough. Either wear a backpack with water bottles inside, or get a fancy Camelbak, an insulated waterbag you wear on your back.
When in doubt, walk. Mountain biking can really be dangerous. If a hill looks too steep or a curve too tricky, get off.
Pick up after yourself! That includes bits of your bike that might get broken off as you speed around trees.
Yield to every non-wheeled creature you pass. The war between hikers and bikers rages on, and the more bikers who slow down as they pass and say something in warning (in the "Excuse me. What a nice afternoon,'' vein as opposed to "Outta my way!''), the better the relationship will be between us.
Don't go off the trails. In addition to messing up the wildlife habitats, you also can hurt yourself. And after a rain, don't go out on closed trails. This erodes the trail and ruins it for everyone else.