For exploration/adventure, try Adventure[0].
For skill games, try Nidhog[1].
For a good recent psychologically engaging game, try Firewatch[2].
A spattering of other favorites: Legend of Zelda: Link to the Past, the Jak and Daxter series, Antichamber, Dishonored, Skullgirls, all of the 2D Mario titles, Final Fantasy Tactics, Smash Bros, Minesweeper, Dwarf Fortress, Tony Hawk's Pro Skater 2
[0] http://www.2600online.com/adventure.html [1] http://store.steampowered.com/app/94400/ [2] http://store.steampowered.com/app/383870/
Care to share some of your favorites? I'd be curious to check them out.