To stray away from all the "points" and "gambling" games.....
Two formats that I really enjoyed playing that made me look at a course a little differently that can be fun to play on occassion...
Red, White and Blue (or whatever color your tee boxes are) - Basically, choose 6 holes to play from the blue tees, 6 from the white and 6 from the red. Or vary it if you have more sets of tees. This is good to play at a course you play often, and as some sort of competition, as the whole fun is the strategy in trying to pick which tees will give you the most advantage on which holes. Also interesting to see how different players pick, perceiving the different advantages (i.e. short hitter choosing forward tees on par 5 to reach in two, while a long hitter will wait and pick a short par 4 to move up on to try and drive the green)
Tin Cup - Made this up in college (though I'm sure I'm not the first), to play 9 or 18 with ONLY your seven-iron. Just like in the movie when Coster breaks every club but his seven and then finishes out the round even par (or so he claims). It's fun to see how simple and insignificant the tee shot feels on most holes "laying up" with a seven, but the game around the green has to get very creative. Additional bonus: it's the easiest way to walk the course, no bag to lug around! Just grab the seven and go. And yes, you have to use it for putting too.