The best cure for a hangover is not getting drunk in the first place.
There are some fun and interesting answers so far, however after doing a little more research on the subject, it looks like there are many "Wives' Tales" (urban legends) for a number of answers such as taking a cold shower, having someone strike you (that's also called battery), eating Lucky Charms, taking over-the counter pain killers, drinking more the next day or combining one alcohol with another kind of alcohol.
What are "Wives' Tales?"
http://en.wikipedia.org/wiki/Old_wives%27_tale
What is "battery?"
http://legal-dictionary.thefreedictionary.com/Battery+%28disambiguation%29
Some parts of this post have been edited to address some of these popular myths.
So let's take a look based on actual independent support for causes and any alleged cures:
1. The body loses most of its water soluble vitamins (Vitamins B1 to B12 and C) from high urination. Those need to be replaced. Vitamin B6 especially.
http://en.wikipedia.org/wiki/Vitamin#List_of_vitamins
http://www.alcoholic-rehab.com/alcoholic_rehab/heavy-drinking-depletes-body-of-essential-nutrients.php
2. It is suggested that water is good to rehydrate the body.
http://www.cnn.com/2010/HEALTH/03/17/alcohol.hangover.cures/index.html
However drinking lots of water will not rid the symptoms of alcohol, or "flush the alcohol out of the body." Alcohol is processed by the liver.
"About 90-98 percent of alcohol that you drink is broken down in your liver."
http://www.mydr.com.au/gastrointestinal-health/liver-and-alcohol-breakdown
Caffeine:
Some people seem to think that caffeine is a solution to a hangover.
Caffeine is a stimulate and alcohol is a depressant. So part of the body is slowing due to the effects of alcohol, and the body is also being impacted by the effects of caffeine. This is like a storm in your system. Taking stimulates and depressants together in any form probably are not the best idea.
According to the U.S. National Library of Medicine,
"...too much caffeine can make you restless, anxious and irritable. It may also keep you from sleeping well and cause headaches, abnormal heart rhythms or other problems."
http://www.nlm.nih.gov/medlineplus/caffeine.html
So if one is trying to sleep off their hangover, or stop a headache, caffeine does not seem to be a viable solution.
ADH:
ADH's purpose is to help the body retain more water in the blood stream, and less excreted in the urine.
http://www.montana.edu/wwwai/imsd/alcohol/Jace/Final%20Drafts/kidney.htm
The Mayo Clinic states that "Hangovers are caused by drinking too much alcohol."
http://www.mayoclinic.com/health/hangovers/DS00649/DSECTION=causes
Further, "Hangover symptoms typically begin when your blood alcohol drops significantly and is at or near zero."
http://www.mayoclinic.com/health/hangovers/DS00649/DSECTION=symptoms
It is true that alcohol influences the hormone ADH, causing people to urinate more frequently, however ADH is not the only cause of a hangover. There are other contributing factors to this effect.
Other Causes of a Hangover:
1. "Alcohol irritates the lining of your stomach, increases the production of stomach acid and delays stomach emptying. Any of these factors can cause abdominal pain, nausea or vomiting."
2. "Alcohol can cause your blood sugar to fall. If your blood sugar dips too low, you may experience fatigue, weakness, shakiness and mood disturbances."
3. "Alcohol causes your blood vessels to expand, which can lead to headaches."
4. "Alcohol can make you sleepy — but your quality of sleep will decrease. This may leave you groggy and fatigued."
Source: The Mayo Clinic
http://www.mayoclinic.com/health/hangovers/DS00649/DSECTION=causes
Aspirin & Acetaminophen:
With regard to taking Aspirin or Acetaminophen (Tylenol, etc.), that may not be the best strategy.
"A small dose of an over-the-counter pain reliever may ease your headache. But there are a few caveats. Aspirin can irritate your stomach. And if you sometimes drink alcohol to excess, acetaminophen (Tylenol, others) can cause severe liver damage even in doses previously thought to be safe."
http://www.mayoclinic.com/health/hangovers/DS00649/DSECTION=treatments-and-drugs
"drugs in this category may also cause liver injury if taken in excess in combination with another hepatotoxic substance, such as alcohol."
--- Melissa Palmer, MD
http://www.liverdisease.com/medications_hepatitis.html
It seems the popular answer thus far has been what causes a hangover, but the question is "What’s the best way to cure a hangover?"
The answer seems to be that one can take action to try and reduce the hangover symptoms such as:
1. "...Water or fruit juice to prevent dehydration. Resist any temptation to treat your hangover with more alcohol. It'll only make you feel worse."
2. "...Bland foods, such as toast and crackers, may boost your blood sugar and settle your stomach. Bouillon soup can help replace lost salt and potassium. Foods and drinks that contain fructose, such as honey or fruit juice, may help your body burn the alcohol faster."
3. Sleep it off. "...If you sleep long enough, your hangover may be gone when you awaken."
Source:
http://www.mayoclinic.com/health/hangovers/DS00649/DSECTION=treatments-and-drugs
The science seems to argue that these "cures" really will not stop the effects of intoxication of the brain.
A 2005 study published in the British Medical Journal said that there is “No compelling evidence to suggest that any complementary or conventional intervention is effective for treating or preventing alcohol hangover.”
http://www.bmj.com/content/331/7531/1515
Thus the "best cure" seems to be to "limit ones alcohol intake."
Alcohol Safety & Motor Vehicles
One should also NEVER operate a motor vehicle if they intend to be drinking alcohol.
According to MADD, "In 2008, an estimated 11,773 people died in alcohol-impaired traffic crashes."
http://www.madd.org/Drunk-Driving.aspx
"Three in every 10 Americans will be involved in an alcohol-related crash in their lives."
http://www.madd.org/Drunk-Driving.aspx
The costs of a 1st time DUI (Driving Under the Influence) can cost close to or over $10,000 depending on laws in a particular state.
"DUI: The $10,000 ride home"
http://articles.moneycentral.msn.com/Insurance/InsureYourCar/DUIThe$10000RideHome.aspx
"Cost of a DUI"
http://www.friendsdrivesober.org/alcohol_drugs_driving/cost_of_dui.html
This may be useful from the University of Oklahoma, Police Dept.
"Blood Alcohol Content (BAC) Calculator"
http://www.ou.edu/oupd/bac.htm
Final Note:
I know this was long, but it is also factually support. My intent is if this gets out to enough people and even if just one person reads this and decides that they will not drink and drive, then it may just save their life and the lives of others on the road.
general question:
Do people thumbs dn because they don't like the answer or because the answer is not factual. In psychology, emotional answers are rarely the best answer. I have tired to support the majority of my answer using 3rd party credible references to help educate, verses post bias or unsubstantiated opinion.