I don't think that aspirin can be put in the category of a "cure". It may stop a mild headache or aches and pains, but it doesn't prevent another one from occurring. The body continues to have the same problem and then reacts again with it.
I guess penicillin and antibiotics were the only drugs to actually cure anything. But then you could argue with me that those drugs don't prevent the body from getting another infection. However that usually isn't the same infection recurring, although in some cases, it takes a change of the antibiotic to actually cure the condition. In fact bacterial infections have become so drug resistant that one antibiotic often leads to another.
I think drug companies are in it for one thing: Money. Note all the advertising urging you to tell your doctor how he should prescribe for you. Just wait until you get the bill for that new brand name prescription, that is if you are lucky enough to have prescription drug coverage. Most insurance companies put the drugs on a "tier" system, and unless you take a Tier 1 generic, you are going to pay out the nose for a prescription anyway. If you have to pay for one on a Tier 4 or 5, be prepared to sell your car to pay for it. Besides, many of these drugs not only don't cure, they may kill.