There were a lot of sleepless nights in my high school days. Since i had plenty of time, i looked up a little bit about sleep disorders and what's considered "healthy" as far as sleeping habits are concerned. The following are my recollections on the research, including intertwined snippets of personal experience.
The sleep cycle is mostly a myth as far as i can tell. Basically it's created by you when you set the hours that you're going to go to sleep and wake up on a daily basis. The cycle is actually created by routinely following the same schedule for sleeping. Small deviations (30 minutes or less) don't make large differences in the short run, but multiple deviations will push the routine out of current synchronization. Large deviations, if not done often (say once every 3 months or so) will make far less impact, because your body knows it can make up for sleep the next evening.
On the other hand, a random sleep schedule basically doesn't know what a small deviation is, because you just sleep whenever. Random sleep schedules don't lead to mental stability, in fact quite the opposite. Your body generally likes knowing that it has some rest coming up, and cataloging your day (a large part of what you do while you sleep) is very important to do regularly. Large deviations on a random sleep schedule put you on your back when they're done because your body doesn't know when it will next get sleep. This is my type of sleep pattern, mostly because i like chaos and randomness ;-)
The main issue with getting little sleep is performance, both physical and mental. Deprivation will tell your body that it is performing up to standards and your brain will concur. You'll be completely wrong, but deprivation also makes the mind a bit more ornery. You wil refuse to see that you cannot perform normally.
Unfortunately, lack of sleep is common. Getting 8 hours an evening really is beneficial. Your mind will be clearer and your day will seem brighter just because your body is truly (not fakely) refreshed. You can cope with less, and everything will seem fine, but things will be slightly fuzzier. Personally, i make certain not to get enough sleep, i like feeling my thoughts like continental drift.
As for the mental side, it has been claimed that you lose 25% of current mental power for every 24 hours you stay awake. So after the first day you're at 75%. After the second you're about 56% there. It gets worse from there. i don't know how intelligent i was, but i have stayed up for a solid week before. i am still an insomniac, but it's getting easier over time...
Finally, i don't know if this one is confirmed, but in theory if you stay awake for two weeks you will die from sleep deprivation. After about 4 days you're supposed to start hallucinating, and 10 days later, for no reason deducible, you die. That's what i've heard, but it might just be hearsay.
Lack of sleep does drop your body's defenses, you will probably have a higher chance of getting sick, but tension and stress also give you a higher chance of getting sick, so sickness is common these days. i don't think there's any one best way to deal with sleeping problems. We're all unique. On the other hand, one can also die of caffeine poisoning, but i'm guessing our eyes would only glow blue if we started giving coffee transfusions starting in pre-K so the little workers could code for us...(joking, joking :-)