How long can humans go without sleep?

Probably 16 hours. Normal humans can probably go about 16 hours without sleep before their brains and bodies start having unusual symptoms. If forced to stay awake, people can probably make it to 36 hours before extreme sleepiness sets in, but they will be acting a bit strangely. It is hard to imagine one making it past 48 hours without training and conditioning to purposely stay up longer.
24-48 hours. Once an individual reaches 24-48 hours without sleep, they become mentally, psychologically and physical irrational, irratic and unstable.