7 days(-ish, I was pretty out of it), at which point I was sedated(was in hospital at the time) with some evil drug that I've forgotten the name of. Apparently going longer than 7days can do some rather bad things to you, never been tempted to find out honestly.
I have Chronic Insomnia, I sleep roughly every 3-4days at the moment. I've grown pretty used to it to now(after 10 years of it), you couldn't tell I was tired til I hit the 4th day usually, at which point my muscles start to ache badly and I can feel myself "dumbing down" for lack of a better description.