It's a few years old now, but Don't Make Love is one of the most memorable experimental games I've ever played. In it, you're one of two oddly-human-behaving praying mantises who are having a hard conversation about whether to breed. It's a hard conversation because they're both very much in love, but know that if they breed there's a really good chance the female mantis will give in to instincts and the male mantis' head off then cannibalize the body. The surreal premise is used to communicate some deeply human feelings.
That's weird enough for you to want to try it, I know, but that's not the experimental part. The experimental part is that the game takes in your typed text in conversation before giving responses. You've got to actually try to shape the conversation and your responses to it by writing your own dialogue—it's the kind of game mechanic that the industry relies on experimental and indie creators to start work on before it can find its way into bigger games.
It's worth saying that it sounds impressive, but you do need to play your part for it to work. The game won't respond well, if at all, to off topic or non-sequitur inputs.
Either way, Don't Make Love is now free on Steam.
I sincerely wish I were writing about the game under better circumstances, but: The game has gone free in memory of principal developer Dario D'Ambra, an Italian indie and art game advocate, who died earlier this year. Collaborators and friends posted the announcement "In Memoriam" on the game's Steam page. "This game was developed by a great human being out of the need to communicate personal experiences, thoughts, and emotions," they say in the announcement. If you're interested in his other experimental and art games, you can find them at the Maggese website.