Fixing wonky wheels

Mountain bike wheels have to be strong, light, stiff, flexible, and above all else round. Every bump in the trail is trying to stop them from remaining this way. Sometimes the bumps win.

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.
The most descriptive term for a bike boo boo – the trail ate your wheel for lunch.
Hub loose
You may not realize that your hub is loose for some time. However, your riding will probably feel “off” – cornering becomes sloppy and descents feel sketchy.
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.