Wear a helmet. Not only will it protect your head, but land owners and managers don't get so anxious about liability when they see people taking responsibility for their own safety. For all-around riding, keep the tires inflated to the maximum pressure recommended on the sidewalls. This provides the most efficient contact between tread and ground, reducing soil disturbance. In deep sand, gravel, or snow, you may need to let some air out for better traction.
Mountain bicycles can also snag weeds.
Keep an eye on spokes, chain rings, and sprockets for stowaways. Check the bike for loose or damaged parts before each ride. If a part breaks or falls off during a ride, pack it out. Stay on roads and trails, and only ride on trails open to bicycles. When it is safe and reasonable to do so, ride out of the obvious and most-traveled line while still staying on the road or trail.