don't listen to anyone else, pick up "Grim Fandango" immediately. one of the greatest games ever made. An absolute adventure, the writing is brilliant, the fun-level is extremely high and it's not super complicated or overly easy. If you like it, check out the "Monkey Island" series.
I also recommend Civilization but it takes some learning, it's hard core, long-hour, turn-based, strategy, but its' way better than any of the other strat or sim games i've tried. smarter and deeper, not just combat or sim-building, full on god-complex escapism.
Image from Grim Fandango. You play Manny, a travel agent for the department of death.
(SERIOUSLY man, you can probably get this game for 15 bucks on ebay, you will thank me)