The good old adventure game genre, seemingly dead today except for perhaps Psychonauts, but the home of so many great games.
My favorite is Star Control II; perhaps a bit more action-oriented than a "pure" adventure game, but still in many ways true to the concept. And, like many adventure games, brilliantly hilarious at times (Zoq-Fot-Pik, anyone?)
And I forgot to mention, for those who don't know already, you can get the game for free for a modern computer as The Ur-Quan Masters ( http://sc2.sourceforge.net/ ), due to the open-sourcing of the original game's code. It runs natively on Windows and Linux (and I assume OS X), and comes complete with all the audio of the 3DO version, too.
Day of the Tentacle was one of favorite adventure games ever, but there was really something special about Grim Fandango. Off the top of my head, I can't think of any other game that combined superb art direction, music, ambiance, story and memorable characters to the same extent as Grim Fandango.
I don't think it's too much hyperbole to say that Grim Fandango was the swan song of an entire genre.
PS The tears of joy box on the very last page was a great touch.