The #1 trouble back country travelers encounter is tire failure. In 80% of all cases it is the right rear tire. Reason for that is that the right rear is the farthest away from the driver and its position is most often misjudged. As a side note: 85% of the failing Firestone tires on Ford Explorers some years back were right rear tires! Indicating that the drivers may have weakened the tire by probably hitting the curb many times while entering the driveway.
The picture above shows the most common problem for dirt road travelers - rocks sticking out of the ground. Notice the entirely blackened left side of the rock - blackened by tires hitting and grazing it. Hit by right tires - as you may have noticed. An off center hit will most definitely destroy your tire.
So, watch out! - Even better, learn how to deal with rocks on the road
This image demonstrates the severe compression when a tire hits a rock off center.
If hit hard enough, the rim will cut the tire. This damage cannot be repaired. Puntures of the sidewall can be fixed, however.
Sometimes you are lucky and your tire survives the hard hit - but your aloy rim does not. The deformed rim does not seal the bead anymore and your tire will go flat. If you are brave and have a really big hammer at hand you may be able to hit back. A couple of good blows will bend the rim back. Most modern aloys allow bending back without breaking.