How bad is it to take Advil or tylenol (acetaminophen) for a hangover?

Not bad. It's not bad, just remember to drink lots of fluids and don't take them on an empty stomach. The better solution is to try and not get a hangover in the first place. You can do this by not drinking excessively and staying hydrated. If you're getting hangovers every time you drink, then you should think long and hard about your drinking habits.
It usually isn't. Unless you have significant liver damage, or a history of ulcers (for advil), they aren't. As long as you stick with label instructions, and aren't on medications which may have drug interactions (in which case you should talk to the prescribing person about it). Hydration and time work best, and avoiding drinking excessively is the best way to prevent it. Chinese study said sprite works.