Oxygen is matter, just like dust or rock or water. As such, oxygen is affected by gravity. Because oxygen is less dense than the other materials that I just named, it tends to float above them, becoming part of the air, along with other gasses in the air (mainly nitrogen). Air only floats because it is sitting on top of other air; otherwise, it would fall to the ground, too. In space, you've ran high enough that there's no more air.

It turns out there actually is oxygen in space! Astronomers determined this in 2011 using the Herschel Telescope. It is thought that the oxygen was originally trapped in the ice surrounding dust and debris that has been floating around. There's just not a lot of oxygen out there. The reason there is so much on Earth is that plants and other photosynthetic organisms generate oxygen through their metabolic activities.