Generally, I have limits, that depend partially on how much sleep I got that night. On a normal school night, when I get perhaps six hours of sleep, I'll start to lose my edge around 12:00. By 1:00 losing focus, and by 2:00 in dire trouble. However, this changes in certain cases. If there is an assignment due the next day, somehow I get hormones pumped through my system or something, and I won't lost my focus. I'll lose my edge, certainly, but not my focus. I can and have focused until well into the next morning before. But these occasions are rare. Another case, on weekends, the threshold will be later. Partially because of more sleep at night, partially because of adrenaline flowing because I'm having fun.
So what do I not do as well in. Concentrating on intelligent activities for one. Doing homework, writing webpages. Gets harder to concentrate. If I'm tired enough, I start writing things that are totally irrevelant to what I'm doing. For example, I remember once when I was doing a chemistry lab writeup, in the middle of a chemical equation, I had written "I had an apple for lunch on Friday" or something. And thoughts start getting shorter and simpler. Sometimes they wander. What else is affected. Driving. I sometimes drive with the window all the way down and music blasting. Not because I'm some kind of punk, but because it is easier to keep my edge that way. Watching boring movies sometimes late at night puts me to sleep. So does reading a book that requires any thinking at all.
On the flip side though, a book that is total trash and has little literary merit, is picked up by me late at night, and it keeps me awake. Or so does a computer game, or a good conversation. Uncanny.
So the moral of the story: If you have something important to do, don't leave it until late at night! That should be play time!