As a rough rule, I can still handle anything from about 1997 onwards. Games like Fallout, Thief, Metal Gear Solid 1, Silent Hill 1 (graphics aged terribly here), and Grim Fandango (though the controls are a pain in the ass) are all OK. And I like playing them as they were.
Prior to that though, it gets tough. Games like X-Com, the original Syndicate, Ultima Underworld, Ultima VII (and I suppose the earlier ones), the early Alone in the Dark games, and the old X-Wing and TIE Fighter games are not very welcoming to me these days. I'd like to see those upgraded to be a little less harsh on the eyes so I'd be more inclined to try them out (or in the case of X-Wing and TIE Fighter, play again).