We have had several dogs, and have gone to several different vets, and they all have recommended aspirin for pain. The rule of thumb is 10mg per 10lbs, no more than 2 times a day and not for an extended period of time. Coated aspirin is the best to give, and with some food. There is the possibility of the same symptons a human would have, stomach upset, ulcers etc..
Rimadyl is a veterinary prescription drug that helps some dogs, but not all dogs tolerate the drug well.