Sega Master System / Mark III / Game Gear
Another one of those ancient oriental games, Shanghai is a sort of Patience game played with tiles. There's a huge pile of these things, and you've got to remove pairs of them and completely clear the table. It might sound easy, but it's not, because you can only remove tiles horizontally, and quite often pairs are covered by other tiles.
Shanghai is one of those games that doesn't look very impressive, but keeps you coming back regularly game after game. It's really therapeutic, and is a great way to relax your brain after a hard day's work.