> Nope. No known stimulants negate the need for sleep
Technically true, but there is a whole class of non-stimulant drugs that do approach this level, without the weird, "amped" feeling of stimulant. Provigil (modafinil) is the best known of these.
Eg: Another study of fighter pilots showed that modafinil given in three divided 100 mg doses sustained the flight control accuracy of sleep-deprived F-117 pilots to within about 27 percent of baseline levels for 37 hours, without any considerable side effects. http://en.wikipedia.org/wiki/Modafinil
I don't have much information on modafinil or other substances in its class so I can't speak to it except to say that the early studies seem promising (I say this as someone who really, really hates the waste of time that is a good night's sleep) despite some reported side-effects.
I would certainly like to see more studies, as well as further information about sustainability. That is, it's great if it really does let you work reasonably well for 3-4 days (within 30% for < 2 days isn't really conclusive), but even then there's the question of what happens after. I doubt you'd just be able to sleep 8 hours and get right back on track.
That being said, my mom was prescribed them for about a decade in the 60's (for weight loss) and she turned out OK.
Nope. No known stimulants negate the need for sleep, nor do amphetamines significantly “increase your clock speed” (certainly not by the amount necessary to counteract sleep deprivation even before the end of your second day).
By the end of day three, you'll suffer from increasingly severe effects of sleep deprivation including but not limited to: cognitive dysfunction, paranoia, and hallucinations (probably auditory at first), plus of course the compulsive behaviour induced by most stimulants.