I'll start with 'sleeping'. For many years, I only went to bed on Tuesday, Thursday and Sunday nights (and then for only a few hours), so I got used to going for several days without sleep. Sometimes I'd skip one of those nights as well but while at college, I found that I couldn't sleep at all for about a fortnight. I went to the doctor, who gave me a few valium tablets. He said to take two at bedtime but, because I felt so shattered (and because I try to avoid taking pills), I thought I'd see if a single tablet would work. It did. I fell asleep at 11.00pm on a Friday and woke up at 9.00pm on Sunday. Unsurprisingly, I was desperate for the loo, so I think that those 46 hours are probably the longest I've been without a pee (or without a drink).
I often forget to eat for a day or two but, since I consume loads of sugary drinks, I'm not sure whether it really counts as going without food.
Chris