Well, here, there's a 6-6-6 tournament (You play 6 holes alternate shot, 6 holes scramble, 6 holes best ball).
There's Wolf - every drives, and the wolf either picks a partner (from the drives) or chooses to go it alone before hitting. If the Wolf goes alone and outscores the other 3, he gets 3 times the points.
There's Bingo-Bango-Bongo: Points are awarded for 1st on the green, closest to the hole (once everyone is on), and 1st in the cup. You can play this both in the foursome, and high point maker across the 12 of you.
There's the 'snake' - anytime someone 3 putts, they get the snake. If 2 people 3 putt, the last one to hole out gets the snake. The snake is given a point or dollar value - he holding the snake loses the points (or owes the money).
We sometimes play 'battle golf' (as inspired by a video game) where if you don't win or halve the hole, you 'lose' a club - the winner decides what club you stop playing with. ie I score 3, the others score 4. I can tell the others which
clubs are no longer used. I usually start with the putter
We use a little red electrical tape on the hosel so we can ID an illegal club (after the honour system stopped working after one guy lost badly two rounds in a row). It's interesting coming to a par 5 where you've got no driver, putter, sand wedge or 3 wood - and there's 550 yards to go.
Depending on the level of golfer, you can play a skins game where, say, birdie or better takes the skin. Pars don't do it. My group usually plays par or better (we're bogey-or-worse golfers).