More obscure ones: Fluxx (fantastic for travel, anyone who can match pics and count to 5 can play with little help), Aquarius (count to 7, very simple).
SET - find sets of 3 cards. Invented by psychologists and will do everyone's head in. V simple to learn.
Bohnanza - a bean-planting and trading game.
Board games: Scotland Yard, Carcasonne (there's lots of expansions to make it more complex).
Perfection is a great elctronic one - put the bits in the holes before the time pops them all up. Marble maze.
Plain card games - Rummy (gin, 500, etc), Black Maria, cribbage, canasta, spit, racing demon...