Final Fantasy 3(VI) on the SNES was probably the first, I played a total of 3 days straight, on the phone the entire time with a buddy, we were having a marathon contest to see who could complete the game first. Deus Ex is probably the most memorable though, as I pulled like 3 all-nighters in the a 5 day time period. Honestly, I've pulled a ton of all-nighters playing video games, some worth it, some not. In high-school, I rarely slept on weekends, so a lot of time was put towards either climbing/hiking, or playing video games. Obviously you can't really climb safely at night, so night times were always video games. Then when I got out of high school, and after I got out of the military, I spent a lot of time playing Diablo 2, and pulled multiple all-nighters playing it, switching back and forth with a buddy of mine. Right now, I consistently play for 3/4 of the night on my DS or PSP, right now it's my DS and Rune Factory 2. I sleep for about 4 hours(from 10a.m. to 2p.m.), then I'm back up for the day.
Oh, also, lol@wingus and SpankyTheElf, I pulled my fair share of all-nighters on FFXI as well, with exactly that mentality "Man, I know this NM is going to pop in 5 minutes, if I go to bed now, I'm going to regret it, cuz it will be the one to finally drop the good stuff" Then 45 minutes later "Well, it hasn't popped yet, so it's GOT to pop soon" then an hour later "Ok, It's nearing the end of it's window, it's literally has to pop in the next 20 minutes" followed by "Stupid NM popped at the last minute of it's window, and it gave me the crap drop! What a bastard! Oh well, guess I better go farm some so I can just buy the damn item instead".
Edit:
Ahh, the good ole days of pokemon on the gameboy color. Using that damn light hook up so i can play under my blanket even tho im suppose to be asleep lol, god how did we manage without backlights?
I had that magnifying attachment that had a light built into it myself, so not only could I see, but it was easier on the eyes since everything was bigger. Pokemon ftw!. Had the same type of thing for my Sega GameGear! Ahh how I loved spending loads of time on Road Rash!