For a great hangover cure -- green tea (iced is better), lots of water, and potassium rich foods to restore electrolyte balance (be aware that frozen vegetables are blanched first, and have no potassium and are lacking many other nutrients). So don't go for the Green Giant if you have a hangover.420 is iffy... It tends to dilate blood vessels, which can make your head throb more. Sometimes it makes me feel better, but take it easy. It can cure the nausea, but a hearty 420-cough can make you puke your guts out.
But yes -- never take Aspirin, Tylenol or Advil if you have a hangover. With all of that alcohol you had the night before, all of those drugs will either shred your stomach or your liver. I know people that pop Tylenol after a long night of drinking, with the idea that it will prevent a hangover. No -- it will just make it harder for your liver to clean up the mess.
I pretty much stay away from most of those OTC drugs. They are ineffective and harmful. Tylenol, Aspirin, Advil have never cured a headache for me.
Caffeine is also great for hangovers and headaches. Many OTC pain relievers (like Excedrin) contain caffeine specifically because it is so good with pain and headaches. Migraine sufferers often consume caffeine when they feel a migraine coming on.
Basically, the throbbing head from a hangover is due to enlargement of blood vessels in your head. Caffeine will shrink those quick-fast and make you feel better, but be aware, it will have a diuretic effect.