Simon - Classic
Simon is a large round electronic box with four player 'press pads' on top. Each of the pads lights up and plays a tone.
The game is basically a memory game. Simon lights one of the coloured pads and sounds a tone, then two, then three, etc. Players attempt to match Simon by pressing the pads in the proper sequence. If someone fails, they get a 'raspberry' and are out of the game. Of course Simon speeds up as the game progresses so it becomes increasingly more difficult.
For a little less randomness, players can set the game to ignore the computer and perform the sequences themselves adding one colour to each play. Player 1 can press "Red", Player 2 then must press "Red" and then adds another "Red", player 3 then must press "Red, Red", and then adds "Blue", etc.