Answer:
There are some conflicting answers, but I've heard that Tylenol is bad for dogs. A vet told me - I'd say that counts for something. So don't give them something like that (or other human medicines) unless recommended by a vet.
I've heard aspirin is OK, but don't take my word for it. I've posted a link to ASPCA and they have an Animal Poison Control section.
The original answer stated that you could give many drugs to a dog with not much worry of harming the animal. That type of answering is kind of reckless. Of course there are several medicines which should not be given to animals, like dogs. Do not give something to your pet because somebody on the Internet said it's ok. Do some real research, call your vet.