The new Humble Bundle just came out, and two of the games you can buy for 1$ are To The Moon and Papo & Yo.
To The Moon is actually more of a visual novel than a game. The graphics are extremely low-quality (which isn't necessarily a bad thing, as it means that its system requirements are so low you could probably play it on a toaster), and the gameplay basically consists of you talking with people. However, its story is fantastic, truly beautiful, and its soundtrack is amazing.
The story is about two doctors traversing through the memories of a dying man to fulfill his last wish. The description from the official site is:
Dr. Eva Rosalene and Dr. Neil Watts have rather peculiar jobs: they give people another chance to live. Literally. There exists a technology that allows doctors to weave artificial memories, such that a patient can request attempts to alter their mind, and wake up with memories of things that didn't actually happen. However, since these new memories are permanent, the conflict between them and the existing authentic memories clash in such a way that it ceases the person's ability to properly function. Thus, the operation is only done to people on their deathbeds, to fulfill what they wish they had done with their lives… but didn't.
Imagine that you could change a choice you made in the past, so that your whole life unwraps in completely different directions. Imagine that you could fix your biggest regret.
And if the premise alone doesn't at least make you curious, the game is worth playing even just for the soundtrack.
Papo & Yo has MUCH prettier graphics, and the gameplay is decidedly more involving. It's one of the most creative games I've ever played, and that's really saying something. You can literally shape the world by playing with it like a child plays with toys. It looks very whimsical at first, but appearances can be deceiving.
Papo & Yo is a story about child abuse, and coping mechanisms, and survival. A child with a violent drunken father finds solace in his imagination, making friends out of toys and bringing drawings to life.
It's not a flawless game. There are some bugs and the gameplay can get clunky. But it's obviously a work of love, something that comes from the heart.
So, these are the two games I wholeheartedly recommend :)