In terms of how high you can go, if you want something to stay above the same spot on the Earth without coming down, though, there IS a distance at which the orbit takes exactly 1 day. This is called geo-synchronous orbit, and there are a lot of communications satellites there. It's about 22,000 miles up, well outside of even the most rarified parts of the atmosphere. So at that point you are really as "high" as you can be without floating off into space.
This guy!
TMI, Dude, TMI!
Hmm, the peer reviews have been consistent.