"Mouth Guards are MANDATORY for stand-up sparring,
and you'll often wish you had one in during Jiu Jitsu training."
Your teeth get knocked together constantly in stand up fighting... even the smallest and most insignificant impact can leave you with chipped teeth. Try getting dates with a broken grill... it's a messy business.
Mouth Guards are one piece of equipment where less is more. You don't need to spend more than a few bucks, and the more rubber you have in your mouth, the harder it is for you to breath.
For that reason, the cheaper the better. The bells and whistles in fancy mouthpieces are just more likely to cut your mouth open. The "Double Guards" with the little hole to breathe through just end up choking your air supply, and believe it or not, your head gets knocked around more since your jaw can't move freely.