Well there is the convention that space starts at 100km up [1] but the atmosphere extends much higher just getting thinner and thinner. For a lot of people space starts when the sky is black during the 'day time' and you can see the curvature of the Earth, but of course that occurs much sooner, like 31km (~100,000') Balloons can reach 100,000' (Baumgartner jumped from 125,000' for example)

[1] http://en.wikipedia.org/wiki/K%C3%A1rm%C3%A1n_line