Coma: To be honest I’m not 100% sure it fits with the rest of the list as it’s been ages since I played it, but it’s a beautiful game with an amazing atmosphere and everyone should play it at least once. Won’t take very long at all!

Loved: A really short game, but it has a lot of replay value in my opinion.

I love psychological games, especially the ones that spur discussions due to their ambiguous nature and the ones with gameplay that reflects the game’s message. Looking up other people’s interpretations to those games is always the most rewarding thing.

Adding:

Don’t Look Back: A short browser platformer that’s a modern interpretation of the Greek myth of Orpheus and Eurydice. Depending on interpretation, the ending can be regarded as either positive or negative, just as many other games on this list.

Braid: Just like Bastion, it isn’t free, and while I haven’t been able to finish it yet, it most certainly meets the criteria mentioned above.

Edit: I realize Don’t Look Back might not actually be fun to play though; I added it mainly for all the interesting interpretations that are made of the ending.

Since there are a lot of people reblogging this… Adding:

Thomas Was Alone: It’s a puzzle platformer with short levels where every character is a polygon shape, each with their own distinct colour, personality, issues (inner battles) and unique abilities that accompany their distinct shape. Though they may not be fond of each other at first, be it because they feel inferior or superior, ultimately, they need to work together to overcome the obstacles in each level. Its minimalistic design coupled with the development of the polygons and their relationships make the game a thoroughly enjoyable experience.

Little Inferno: From the makers of World of Goo, as you might be able to tell from the design! You sit in front of a fireplace and burn toys to keep the fire alive, continuously gaining money to buy more toys to burn. The extremely appealing visuals and effects compel you to keep burning toys (more toys are unlocked from a shopping catalogue as you purchase them, and simultaneously burning toys that are part of special themed combos gets you additional rewards) - until you suddenly realize… (whisper whisper)

Both games are aren’t free, but they’re occasionally on sale (as part of Steam or Humble Bundle sales). 

I’m going to add some as well, since there’s been a lot of very interesting games exploring very meta and psychological aspects of video games recently. 

Papers Please: I cannot recommend this game enough. If you want a game truly about moral choice, look no further than this game. There is no binary moral choice here, no moral choice indicator, nothing video gamey about the moral choice here. Instead, it merely asks questions and lets you answer them according to your own morals. I have learned things about myself from this game. Not to mention, it does not sacrifice engagement for moral choice or narrative. Unlike Cart life, which is the closest comparison I can make, this game is not a slog through the mud.The design is tight, fast-paced, intense, stressful, and somehow fun all at one time.    

Spec Ops: The Line: While this game is a bit on the expensive side, (about a 6 hour game for $30) There has been a book written and published analyzing this game. That in itself should tell you how important this game is. It is all about the modern shooter and everything wrong with it, told not only through the narrative, but through EVERYTHING. The presentation, gameplay, and narrative. This game is incredibly psychological and makes you feel like a horrible person despite the fact that the game never really gives you a choice. I can’t say much else without spoiling it, but get this game. Get this game.It was the most important game of 2012. 

Antichamber: Let’s move away from the ‘games that make you feel like a horrible person’ into a psychological game that is more interested in fucking your mind and defying all your pre-built conceptions and everything you’ve ever learned playing video games. Think Portal in an Escher like maze, no game has made me gasp in pure surprise and delight as this game has. If you are into design, it is a must-play because of all the systems at work and how this game can surprise you without being RANDOM. This game has a logic, it’s just not a logic that we are used to. 

well i accidentally spent 3 hours playing these