The Ubuntu version of Linux comes with 17 games from the international GNOME: Free Software Desktop Project and there are thousands of other games that will run on Ubuntu/Linux.
I've been playing the chess game a lot lately and have completed hundreds of games in the last week or so. Please note that I said "completed" not won. I'm not much of a chess player, but I've been able to beat other computer chess game - but not this one (yet). The computer just doesn't make mistakes and it becomes really addicting to watch the patterns it plays and see if you can figure out a way to outsmart it.
I am up a couple of thousand dollars playing the blackjack game, so that's some consolation.
I'd venture a guess that if you are hoping to keep your mind fit, playing almost any game beats watching most TV.