Mustaches have been key for some games. Both heroes and villains have them.
As a gameplay mechanic
Mustaches reached their hairy apex in 2003's Mario & Luigi: Superstar Saga. In this 2D RPG for the GameBoy Advance, players were given a "'Stache Power" stat which was equivalent to 'charisma' in other RPGs. The higher the 'stache power of either Mario or Luigi, the less they would have to spend on new items, and the more they would recoup from used item sales.
Similarly to this in the recent title Mario & Luigi: Bowser's Inside Story , the "'Stache" statistic is used to increase the critical/lucky hit chance, and to get a winning space on a scratchcard, which returns money upon purchase.
Characters in practically every Mario RPG have something to say about Mario's mustache, often comparing their own to his.