Head Gear is optional at the super 32 and most preseason tournaments are the same way. I believe that if it is a sanctioned High School event that head gear is mandatory. Other than that it is up to the tournament directors whether or not it is mandatory.
Some coaches say that headgear can be used against you by your opponent and I have seen it, but I would hope that our esteemed Referees would catch that.
Although Cauliflower ears have been a badge of honor in our sport, my kids will wear their headgear or suffer the wrath of their mother(ha ha).