Yeah, definitely put Monkey Island right at the top of your priority list. After Grim Fandango, the first three games in that series rank as my favourites of all time, and I'd imagine the same goes for a lot of other people. The graphics of the first two are a bit dated, but the games themselves are truly excellent. I even have a Monkey Island avatar!
Other than the rest suggested in this thread, the Broken Sword series is another that's begging to be played.