Several notes about HORSE the game, in addition to what /dev/joe pointed out.

Horse is about making a better shot yes, but it is also about 60 % mental. Whether or not you are a better player, talking trash and making wildly better shots is really the key to winning. Making the other player mess up is just as good as making the good shots, as long as it's just in good clean fun.

Horse is also a two-player trick mode in Tony Hawk Pro Skater 2. You each take turns trying to perform better tricks starting from the same location in a stage. You try to 1-up each other, until a person messes up or scores less than the previous player. That person gets a letter and the match continues on. A player loses when one person spells HORSE, just as in the basketball game.

The game of Horse was best embodied in a set of very famous McDonalds commercials, where Larry Jordan and Michael Bird play each other in Horse. It ran as a running commercial gag for a while before it was taken off the air. The official name of the commercial is "Showdown". The only rules were set forth was by Larry Bird and was (memorably) "no dunking!" (Bird could never really dunk).

The two would interchange shots, and were so perfectly matched, the shots moved to quite incredible things. It started out on the floor, moved over to the rafters (Bird: "Off the floor, off the scoreboard, off the backboard, no rim" *), and then in the second spot, it had moved outside (Jordan: "Off the expressway, over the river, off the billboard, through the window, off the wall, nothing but net.", *swish* sound here).

It was a quite sucessful commercial spot and ran throughout 1993, airing at the Super Bowl, and continuing afterwards. McDonalds got quite a good value with their money by playing off the highly publicized friendly rivarly between the two, and it has stuck in the mind of all who have seen it.

* Quotes taken from a Google cache of an expired web page