To the Moon is an adventure game developed by Freebird Games, where the player takes on the role of a doctor employed by Sigmund Corp., which offers a wish fulfillment service using a futuristic piece of tech that can create artificial memories. There's just one twist: the doctors have to use the machine to explore their patient's memories Inception-style.
In To the Moon, the player must use the machine to fulfill the last wish of a dying old man: to fulfill his lifelong dream of going to the moon. However, aged as he is, he doesn't remember why, and it's the doctors' job to delve backwards in time through his memories to discover why he wanted to go to the moon before they can fulfill his dream.
If you're looking for one of the best stories that gaming has to offer, then To the Moon is the game you're looking for. You might want to hold off playing it, though, if you're not in the mood to shed a few tears.
(Also, Finding Paradise, To the Moon's slightly lengthier sequel, is now available!)