I agree that the early/mid 80’s is where it’s at for pure score-based, single player, single credit competition.
I always prefer friendly competitions at games where everybody is a complete noob, because in a game like Pac-man, there will always be somebody who knows the patterns and will dominate.
There really was a boom in the 80’s where thousands of great walk-up-and-play games got made but nobody ever heard of them because they got lost in the shadows of the Donkey Kongs and Pac-Mans. Here are some titles outside of the same tired old classics that I’ve enjoyed competing in online and with friends: Tazz Mania, Marvin’s Maze, Anteater, Swimmer, Metro Cross, Solar Fox, Mr. Do!’s Castle, Do! Run Run, Baluba-Louk No Densetsu (awesome game!), Kickle Cubele, Snow Bros., Strikers 1945, Dig Dug 2, Q*Bert’s Qubes, Wacko, Sky Kid, Eyes, Astro Blaster, Pengo, Pooyan, Hopper Robo, Roc N Rope, Rescue, the Glob (aka Beastie Feastie).
If you want a non-fighter multi-player game that actually makes for a fun competition, try Trog. Up to 4 can play. Nice looking graphics and animations, simple addictive gameplay. The players can keep pumping in credits and your score doesn’t reset, so what I’ve done is put no restriction on number of credits used and “race” to a certain score. You can score big in that game with the powerups, so epic comebacks are possible. Plus, you can punch each other in the face for no reason—very cool.