The first game I actually made and finished entirely is a Tetris.
Well, with a little twist. This game had a "rival" function: You could see the nickname and score of the first player that has a better score than you. It motivates you to keep improving to beat some persons. Then you can upload your score in the leaderboard too.
Unfortunately due to changing my server a few years ago the rival functions aren't working anymore, but the game is still playable.