How to make an experience, not a game.

Just wanted to get a discussion going.

So how do we all make a game that conveys a message. Something that you play that doesn’t exactly have to be in depth, but just makes you say, ''Oh, wow that meant something". Something that gives you a good feeling afterwards.

What do you think? What can us programmers do to make a game convey not just gameplay, but a message that may just stick with someone forever?