Carl,
More commonly in the US, stableford is just called a points game. The standard breakdown differs a bit from Ian's; 1 for bogey, 2 for par, 4 for birdie, 8 for eagle, and 16 for an ace. Some games penalize one point for double or worse, but many do not.
I think that this format is used commonly in Saturday morning games at a club, with quotas adjusted each week, either by the club or a "commissioner". Typically, quotas go up by one point for every two over your quota, with a max of a 4 point increase, and go down one point if you fall short of your quota, regardless of how short you are. You can make the payouts anything you want in terms of how many places you pay. The usual starting point is 36 minus your index as a quota for the first three games, then a quota is set based on those three rounds and you go from there. The great thing about this game is that you can have guys playing from different tees with no problems or adjustments. It can also be combo'd nicely with a skins game.
If you have fewer players and no desire to adjust quotas weekly, try "10 Ball", or one of the variations. So if two or three guys are playing against each other in the same group, each guy has to count his score on 10 holes; he has to declare before the next tee whether or not he wants the previous hole to count. If it's two against two, it would be 10 holes each (20 ball); if it's my foursome against yours, it would be 40 Ball. Lots of decisions, keeps everybody in the game, can be played gross or net, etc.
Another obvious game if you have a regular foursome is to rotate partners every six holes; those that don't like the term 666 often call this a California.
If your group is smaller and you have only a threesome, a six point game is a lot of fun. There are six points on every hole; an outright winner gets 4 points, with a second place tie between the other two players getting one each. A clear second would be a 4-2-0 split; two tie is 3-3, and all tie is either 2-2-2 or 0-0; it comes out the same. Again, keeps people in the game because a bad hole doesn't kill you, and it can be played gross or net.
Hope that helps.