It's no secret that I'm a huge fan of anything game or game-like. I'm especially fanatical about independent (indie) games. They are games that are usually developed by a very small team (often just one person) and that are self published. These games are generally more experimental and innovative than commercial ones -- this is because they cater to a smaller niche and can afford to try something new. So without further ado, here's some of my favourite indie games of the past couple of years. I'm sure I've missed some, but it's a start.
Samorost 2. A classic point&click adventure set in a strange, organic, beautiful world. Also check out the developer's latest game: Machinarium.
Captain Forever. A combinatorial design abstract space shooter.
Iji: A classic platformer+rpg developed by one guy over a number of years. Amazing stuff!
Windosill: A short puzzle game with beautiful and imaginative objects.
Facade: You arrive at your friends' place while they are arguing. Interesting concept and execution.
Passage: A short, poignant statement about life, with a retro aesthetic.
Knytt Stories: An adventure game with an excellent minimalist aesthetic.
Gravity Bone: Very amusing spy game. Definitely worth a play, will only take a few minutes of your time.
Eufloria: This game is in my list because of its minimal aesthetic. Used to be called Dyson, a reference to Freeman Dyson's idea of what life might be out in the asteroid belt.
Today I Die: I read that someone described this game as visual poetry, and I guess I agree. Melancholic.
Dwarf Fortress, Linley's Dungeon Crawl: Some more excellent games, but definitely for the more hardcore RPG/hack fans.
Hotel: A story of several people visiting a hotel. Very surreal.
Psychosomnium: This stands out for me amongst all of Cactus's games. A crazy mess of code and programmer art. Poses some questions about our expectation of games.
I've provided links for some of the games, the others should be easy to find by googling. For more games, try TIGdb, or check out last years winners of the IGF.