Around 4 days, and I'm estimating around 90-93 hours with no sleep. I was 19.
I was studying for exams. I had 3 exams in 4 days, and they included Chemistry and Biology. I suck at Chem, and for some reason, I wasn't doing well in biology. Lets just say that I'm was a very persistent person, I had around 7 days to study for 3 exams, and I don't give up easily.

After the 1st night, I felt like a zombie. On Day 2, I got my second wind and felt fine in the afternoon of day 2. By Day 3, I was tired but I didn't need to sleep.
Day 4? Same. I even felt fine after I finished my last exam. Then I packed my bags, brought everything over to my car, and it was around 2 AM. I was going to drive home. I felt wide awake, and completely OK. My eyes felt bruised or something, but i didn't feel "tired". For the first 20-30 minutes in the car, I felt on top of the world, and really excited about finishing my bio exam. After 45 minutes, I was in serious danger of falling asleep and crashing my car. In fact, my eyes felt heavy, and closed quite a few times while I was driving. Uh oh. I didn't feel tired until I was allowed to sit continuously in my car, despite the music I had at full volume! Anyway, I opened up my windows and turned my music on really really loud. Didn't help. I pretty much fell asleep, so I pulled over, pinched myself as hard as I could on random parts of my body, and got out of my car for a breather. It helped a bit.......just enough for me to get home. I zonked out after that for a good 12 hours or so, and still felt exhausted. I spent the next 2 or 3 days sleeping well at night, and taking 1 or 2 hour power naps during the day to recover.
I'm 28 now, and I occasionally still stay awake for 40-50 hours without sleeping. I'm guessing around 12 times per year?

That's how I roll.