V-Brakes rubbing
Apart from wasting power, gritty brake pads can wear through a rim very quickly, so fix them!
Disk rotor bent
Just dropping the bike on its side can bend the rotor. Crashing it can bend it severely. Make sure you take your time to get it straight again.
Hydraulic brake hose broken
It's surprisingly easy to rip out a hose by catching it on branches. It's often possible to put it back together again afterwards.
Brake pads worn out
When was the last time you checked your pads? Don't wait until you hear metal-on-metal.
Contaminated (oily) disk brakes
Disk brakes work really badly when they get oil on them. What is hydraulic fluid? Oh yes, it's oil.
Broken brake lever
Even if the lever's gone, the brake can still be made to work.
Snapped or frayed brake cable
If it broke in the right place, you can fix it well enough to use on the way home.