7th Guest and 11th Hour are great puzzle games that'll frustrate you in good ways. (For any iOS users seeing this, do NOT download the iOS version...awful awful port).
If you don't mind adventure games, as others have suggested anything Sierra did was great. I recommend the lesser mentioned Colonel's Bequest & Dagger of Amon Ra which are both murder mysteries and Freddy Pharkas Frontier Pharmacist which has some reasonably questionable and hilarious comedy. (I've also heard great things about the Gabriel Knight games but have never had a chance to play them.) Or if horror is your thing check out Phantasmagoria for 7 discs of somewhat campy, ridiculously gory, banned in several countries amusement. Return to Zork was also fantastic even if you'd never played the original Zork games.
Also kind of a weird one but I really liked playing Inca. You're an Inca (surprise!) who....has a spaceship and fights Spaniards in space and stuff. Because reasons.