Oh boy, time for me to list a bunch of weird games I love. I'll leave off anything current gen since sequels may be in the works for them.
Henry Hatsworth in the Puzzling Adventure
Harvey Birdman: Attorney at Law
Hotel Dusk: Room 215
Elite Beat Agents
World of Goo
Cave Story
ZombiU
I would include Teslagrad, but it just got a sequel announced to be in development.