Source: http://what-if.xkcd.com/134/

Q: "...what would happen to my body in orbit over the course of years, decades or centuries?"

A:

"If you tried this, the first thing that would happen to your corpse would be that it would dry out... you'd become a freeze-dried mummy, after losing about 80% of your body weight in water."

"If you're in an orbit that passes near the Earth, your orbit will quickly decay, and before long you'll re-enter the atmosphere and burn up."

"If you're in a slightly higher orbit, you'll last longer, but you'd also be in the zone where space debris was thickest... you'd probably have a violent collision with something."

"Higher orbits are safer... You could spend centuries drifting among TV broadcast satellites."

"If you wanted to last even longer, you could launch yourself away from Earth completely, finding a quiet and stable orbit somewhere in interplanetary space. There, over the course of millennia, you'd be slowly baked by the Sun's radiation and pitted and powdered by micrometeorites."