What are effective prescription drugs for chronic pain?

Many options. Chronic pain can be difficult to treat. What works for one person might not work for someone else. If you have chronic pain it is best to see a pain specialist to go over the various options. Some would include nsaids and anti-depressants. Narcotics are usually a last resort due to the risk of dependence, tolerance, and addiction.
Depends on cause. There is no single answer. For neuropathic pain medications like Cymbalta (duloxetine) and kyrica may help. For fibromyalgia muscle relaxers and exercise help. After a broken bone an opioid may help. With arthritic conditions (or other inflammatory causes) an anti-inflammatory is best.