Portal, Portal 2, Shadow of the Colossus, Halo, Minecraft, Terraria, Magicka, Just Cause 2, Battlefield 3, Borderlands, Realm of the Mad God, Nitronic Rush, Tribes: Ascend, Bastion, Sanctum.
Portal and P2 are great puzzlers with equally great humor. SoTC has some of the best boss fights ever, and is one of the most immersive games I've ever played. Halo is Halo, has an interesting story if you're willing to do a bit of digging (no pun). Minecraft is a great sandbox, and the mods really open it up for craziness. Terraria is basically 2d Minecraft but with a lot more stuff. Magicka is a great coop adventure, but bring friends that aren't going to instagib you. JC2 is another great sandbox. BF3 is just a solid shooter. Borderlands is ARPG meets FPS, and it's a lot of fun, if repetitive. RotMG is... a coop mmorpg bullet hell fantasy shooter. Go watch some gameplay. Nitronic Rush is a great racing game with a Tron-esque aesthetic and pretty nice music. Tribes is, well... Tribes. Go watch some gameplay. Bastion is a fantastic hack and slash RPG with a good story, great music, and the best narration ever. Sanctum is a FPS Tower Defense that's a lot of fun with friends.
Out of all of those, the best are Portal 1 and 2, Shadow of the Colossus, Bastion, Minecraft, Terraria, and Nitronic Rush.