So...no real time strategy, horror games, race games, rhythm games or roguelikes?
Still...there's a lot to choose from. I also agree to most games already mentioned (I've not played all of them. And just qube is just...it's too boring for my taste).
Let's see...from my favorites:
-another perspective (platformer/puzzle game)
-antichamber (abstract first person puzzle)
-braid (platformer puzzle...a classic for good reason)
-brothers - a tale of two sons (you really need two analog sticks, though)
-cook, serve, delicious (sort of a restaurant sim...it's a click fest, but insanely fun)
-duet (just youtube it to see if this sort of game excites you...it's great, but perhaps not for everyone)
-pac-man (no need for an explanation, I hope
)-plants vs zombies
-super hexagon (beware: this one is TOUGH)
-VVVVV (minimalist platformer. Great soundtrack)
-anno 2070 (a must if you like city-building games)
-rollercoaster tycoon games (classics...you can find most of 'em on GoG)
-roundabout (rotating taxi simulator in the '70s. Hilariously fun, but I admit the chances of it getting bloody are...well...high
).-jazzpunk (1st person point 'n click. It's HILARIOUS. Has a couple parodies on action games, though)
-oddworld: abe's oddysey, and abe's exoddus. The newly released new and tasty (a remake of the original) isn't bad, but...ah, choose for yourself
-thomas was alone: simple abstract platform game. Great narrative
-mirror's edge. Yes, it has some combat in, but the goal is the freerunning.
-element4l: a platformer parkour game. It gets addicting fast
-contraption maker: probably the best puzzle game ever made. And at the very least the most entertaining to watch in action.
