If I could only choose one piece of protective gear to wear on the mat it would be the humble mouthguard. Grappler’s faces are always getting banged up, even if they don’t practice mixed martial arts. Whenever there is a scramble to pass the guard, to escape a bad position or to apply a submission there is always the possibility of getting hit in the head by an errant leg, head or arm. I have trained both with, and without, a mouthguard and have learned my lesson repeatedly. Nowadays I spar with one in at least 95% of the time.
Mouthguards protect you in many ways: they stop your teeth from chipping or getting knocked out, they reduce the likelihood and severity of biting your own tongue, and help prevent concussion. By offering you something to bite down into it also makes it harder to break or dislocate the jaw, should something hit you really hard.
If you decide to wear one you should try to wear it all the time while sparring. If you only put one in for competition you may find that it interferes with your breathing. If you become used to it in ‘regular’ sparring you will find that it bothers you much less when you’re really going hard. Not that I’m recommending this, but keep in mind that some boxers do their roadwork while wearing their mouthguard, just to become accustomed to breathing hard with it in.
The basic “boil and bite” mouthguard is usually available for about $5. Although there are mouthguards that protect both the upper and lower teeth, I recommend starting with the style that mounts only on the upper teeth.
If you can afford it (or if you have a good medical plan) custom-made mouthguards are way to go. Your dentist can take a mould of your teeth and have a sports-mouthguard made that will fit you perfectly. This is not a cheap option: I have heard of dentists charging anywhere from $50 to $150 to do this, but once you’ve tried these mouthguards you’ll never want to go back.