A game about my avatar? How about, OH MY GOD PLOT INCOMING!
You play as an astronaut, doing SCIENCE on the ISS, and then you go out on a space walk for some routine maintenence when suddenly something goes horribly awry! The tether that keeps you from drifting out into space breaks (somehow) and you are doomed, you float through space for a short time, before a WORMHOLE opens up, sucking you in, (the "In the Wormhole" sequence would be really trippy) and when you wake up a short time later, you awake on the surface of an alien planet, and you must use your wits to survive the hostile enviroment.
It'd be sandbox-y, about trying to survive day to day in an alien enviroment, and maybe there will be some primitive natives, so there are other characters to interract with, I dunno'.
Yes. Yes. Yes.
Or maybe, the whole space stuff happens, but instead of waking on an alien planet, you awake on earth, in the earliest days of mankind! And through some wierd (possibly supernatural) means, you are immortal. And it's about you experiencing different stages in the history of man, until eventually you catch up with the time you were alive in the previous history, and through some weird coincidence, you wind up doing the same thing you did in the previous history, becoming an astronaut and then going out into SPACE on the ISS, to do SCIENCE, and then you go out on a space walk for routine maintenence, THUS WINDING UP EXACTLY WHERE THE STORY BEGAN! You are told by your astronaut pals that you kind of SPACED (pun-tastic) out for minute or so, thus rendering the entire thing a hallucination/dream, and not real. MINDFUCK.
Or... WAS IT? You have a vivid memory of everything that happened, and you can suddenly and inexplicably speak a number of extinct, ancient languages. Still, nobody believes you, thinking you just went crazy or somesuch, and after awhile you begin to doubt yourself, maybe you really are crazy? AND THEN, AS IT HAPPENS, you have in your possession a keepsake given to you by your ancient Egyptian/Greek/Babylonian/Whatever love interest thousands of years ago. THUS VINDICATING YOURSELF. Hurray, happy ending.
Come to think of it I doubt this would work as a game, still. Thats the first thing that came to mind, oddly enough.