Yes, tramadol is used to treat moderate pain in dogs on a short-term basis, but it was initially developed for human pain. It's not something you want to give a dog without the advice of a veterinarian.
Tramadol is : http://www.medicinenet.com/tramadol/article.htm
In dogs and cats : http://www.1800petmeds.com/Tramadol-prod11064.html
I personally don't think it worth taking so it probably would be more desired by a pet. No really it is a pain reliever for temporary relief of back pain sprains bruises etc.. The best advise I can give is take OC (over the counter) pain relievers, they have a better chance of getting rid of your temporary pain, and no addiction. Go for the fastest, safest pain relief. Its kind of like marriage/ divorce: people give up/in to quickly sometimes you need to feel the pain to appreciate what life you had before addictions. Don't become a statistic....