Surprised to only see this mentioned a couple of times in here. This and the sequel are probably the two games I would recommend everyone play, gamers and non-gamers alike. They're just that good and easy to get into from a controls perspective.
If I'm going to recommend old games, it'll be mostly games from the age of Intel Pentium 3, before all this newfangled multi core stuff they're up to these days. Anything that comes after that is someone else's to go to bat to. Heck I was playing Doom for a few years at a cousin's house before we had our family computer in 98