I'm all for storytelling when it comes to my favourite games:
The Secret of Monkey Island
Monkey Island 2: Lechuck's Revenge
Sam & Max Hit The Road
Anachronox (a true underdog)
Psychonauts (that bubble blowing teleport creature is just too cute)
Silent Hill 2 (such a shame the fist game won't work on my computer
)
Half-Life 1 (I really enjoyed 2 (especially with all the mods), but it just didn't get to me as much as the first)
Morrowind (also made a much bigger impression on me than Oblivion, even though I'm still an Oblivion addict (mods, more mods!).. first cut remains the deepest I guess)
Soul Reaver 1 & 2
Unreal
Gabriel Knight
The Legend of Kyrandia (the first)
Simon the Sorcerer 1 & 2
Little Big Adventure 1 & 2
But some are just plain ol' fun:
Tomb Raider 2 & 3 (2 is better, but 3 was my first)
Blood
GTA Vice City
Doom
Prince of Persia (the very first ofcourse)
Wolfenstein 3D
The Incredible Machine
Settlers 2 (gold)
Stunts
Tropix
Peggle Deluxe
Audiosurf
Need For Speed III
Scorched Earth
Non-PC games:
Paratrooper (C64 version)
Lazy Jones (C64)
Super Paper Mario (Wii)