I have never had a hangover, but I have heard that they happen partly because you become dehydrated because the alcohol acts as a diuretic, so drinking a lot of water or something like a sports drink to also replace electrolytes before you go to bed should help prevent one. That is what I have done on the rare occasions when I have had more to drink than I should have.
Also, I think there is something in the darker colored alcoholic drinks (red wine instead of white, bourbon or rum instead of vodka, etc.) that makes hangovers more likely.
The problem with Excedrin is that it contains aspirin, which could further upset your already upset stomach; acetominophen, which could cause liver damage if taken with alcohol or if you are a heavy drinker, (more than three drinks a day); and caffeine, which will increase dehydration.
I think that Ibuprofen is a somewhat safer choice.