First of all, here is my favorite mouthguard for braces. It is designed to fit over the braces, so no need to boil it and bite into it. It is very comfortable and also adjustable. They also come with football straps for the football players. You can buy these online or at Dick's Sporting goods.
Now for the question "How do I know if I need to wear a mouthguard?"
Basically, everyone in sports should be wearing them. You need to PROTECT YOUR TEETH AND SOFT TISSUES (lips, cheeks, etc)!!!
What sports?
1. Hockey
2. Football
3. Basketball
4. Soccer
These are the more obvious sports and are required in order to play football or hockey. For basketball and soccer, there are chances you can get elbowed in the face, hot with a ball, so best be safe than sorry!!!
In addition, I would recommend wearing a mouthguard for:
1. Baseball/softball
2. Gymnastics
3. Rigorous cheerleading (practices only)
4. Any other sport/hobby in which there is a danger to your face
I cannot stress enough that it is not worth NOT being safe and risking a potentially serious injury. The mouthguards are nice and breathable, adjustable, and they feel very comfortable, so getting used to it is the only tough part.
Let us know if you have any questions!
