I stayed awake for approximately 85 hours once -- in order to sit 18 hours of exams over three days at the end of the first year of my engineering & computer science degree.
I wasn't a very diligent student in my first year. (I spent most of it programming instead, and the internet was brand new to us as well. Both were addictive. So I ended up doing that instead of studying the degree materials.)
When the end of year exams came, I hadn't really done much revision.
The night before the first day of exams (6 hours of exams - two subjects, one in the morning, one in the afternoon), I decided to stay up and study for a change, which is what I did.
Lunchtime that first day was spent preparing for the second exam.
Phew, those went ok, then I realised I didn't know enough about the next day's subjects either, and did the same again.
And again the third day.
Amazingly, after the third day of exams (about 78 hours awake), when it was time to relax, I felt so relieved that I felt light and great. Went out to the pub with friends, and wasn't tired at all, which surprised me.
Slept quite normally that evening.
I can confirm, the hallucinations after multiple all-nighters are quite real. Dreams seem to keep trying to start up, speech is slurred, and things get strange. Yet somehow, in the midst of that, I was able to write adequate answers in difficult, long technical exams.
The hallucinations, and the slurring and reduced physical coordination, seem to go away in the "relaxed" phase after something is finished. It's like the relief makes a new wave of physical resources available to work with.
I've done a few highly-stressed all-nighters (and sometimes 2 or 3 nights in a row) since then (due to hard life events than bad planning on my part). I've also been up 4/5 nights (I can't remember which, it was a very stressful event), but got short (Although the exams 3 nights 4 days awake for exams was a kind of success, and it might seem like I must be one of those people who doesn't need much sleep, the opposite is true.
The longest time I've slept straight through, without waking (except for the usual wake-and-roll-over-back-to-sleep moments), was 25 hours. I'm sure, because I decided to find out when I was a student (a bit older than the above story). I knew that I slept a long time generally, and needed to if I was to feel rested, and that the timing was unpredictable. One day I decided to just sleep and sleep until I felt completely rested, and see how long that would be. So I did that, and it was 25 hours before I felt like I'd had all the sleep I could take. It felt pretty good, though waking at midnight, having gone to bed the evening of the day before, made me feel isolated.
I spend most of my life feeling rather tired, and I need about 9-11 hours sleep to feel good the next day (it varies but 10 feels like the average), but it's rarely achievable, for social and work pressure reasons, as well as difficult to predict insomnia. I've had fairly chaotic sleep "cycle" since the age of 15, which started due to staying up at night to do homework from school, and has never really recovered. By chaotic, for about 20 years (until ~35) most days it was unpredictable to me when I'd sleep and when I'd wake. Which as you can imagine, made work difficult.
Since 35 it's been more regular in that I sleep almost every night, although not always the same times. Sometimes I'll wake up in the middle of it, and sometimes I won't get to sleep at all, despite everything being dark and quiet and comfy, and me being tired. If I get sleepy and think I'll sleep, I need to go to sleep or I risk missing the "window" of opportunity to fall asleep.
I would love to feel rested some day. I can't remember the last time I felt like I had a really good sleep and was fresh and rested the next day.
(ps. None of the above involved any drugs, not even legal ones, unless you count Coca Cola. I didn't even drink coffee in those days. Saying this upon seeing the other comments about speed/meth etc.)