If you HAVE a hangover... Ibuprofen and co-codamol are the best painkillers to take in combination. Three analgesics in one go. I won't mention brand names because they differ between countries and it really fucks me off when people use brand names.

Just read the label to see what is in it.
If you're under 16, don't take aspirin due to increased risk of Reye's syndrome.
Drink as much water as possible. Juice. Cordial. Tea and coffee are fine. The mild effect of xanthines really don't have much effect if you're drinking enough. Caffeine is added to some pain killers in order to make paracetamol work faster/better plus the perk isn't such a bad thing.
If you are sick, try rehydration salts. If you have the squits, make sure you didn't eat anything dodgy in your drunken state because you want to flush it out of your system, rather than keep it bunged up inside of you. Just let it flow if you suspect a dodgy kebab or some poor home cooking.
If you just feel sick, try an antacid or something with a similar effect. Booze doesn't do much good for your stomach, so just try and settle it down.
Make sure you don't drink with certain drugs. Anxiolytics can enhance the effect of alcohol and leave you feeling a bit worse for wear (you might not remember what you did the night before or you might try something a bit stupid). I wouldn't bother with alcohol if you're on any drug which works on the brain though. One drink with the antibiotic metronidazole (usually given by a dentist) inhibits the break down of alcohol, so you get a hangover effect very quickly.
Some people swear by charcoal tablets, but they are usally about 70. They do work to some extent though, but only BEFORE you get the hangover.
Non-medicinal methods I found which work:
1) Sleep - I've slept for 16 hours straight before and felt nothing but hunger and the need to go pee when I woke up.
2) Long hot shower - I've often felt better after a long shower.
3) Playing video games - I quickly forget I have a hangover as long as I have nothing to do all day.
4) Hair of the dog - It does work. I don't care about the theory. Apparently it is along the lines that by drinking more alcohol, you speed up the metabolism of alcohol in the system after sleeping. I don't trust this, but drinking smaller amounts the next morning until you have regained some senses and then sleeping again has helped a few imminent mind-erupting hangovers in the past.
5) Working - For some reason, no matter how hungover I was, the concentration of working and dealing with customers always made me forget how rough I felt.
If all else fails and you have people you live with:
Milk it for all it's worth.
'OOOOOH! I REALLY NEED A DRINK! Mmmmm, could you get me one?"