Spoke breaks
Metal fatigue or big sticks can be to blame. Straighten up the wheel and ride on.
Ripped tire sidewall
Sharp rocks can gash tires. Then the tube splurges out like a hernia. Not conducive to riding.
Flat tire, no spare tube
This should be enough to teach you to bring spares. However, you can use what you have or natural resources to ride out.
Taco
The most descriptive term for a bike boo boo - the trail ate your wheel for lunch.
Loose wheel hub
You may not
realize that your hub is loose for some time. However, your riding will
probably feel "off."
Rim worn through
Rims give up at odd times, like when you are just riding
along, or when the bike is sitting on your car after a ride.