Kardashev scale
en.wikipedia.org
en.wikipedia.org
Edit: Here's a link to the ST-TNG episode: http://en.wikipedia.org/wiki/Relics_(Star_Trek:_The_Next_Gen...
There's been some speculation that the integrity of a Dyson shell (the thing most people know as a Dyson sphere) could be maintained by basically running large masses in orbits along the shell. Again, it would be a little inefficient (you're using some of the star's energy to power "not collapsing"), but we don't necessarily know it's impossible.