I have found for myself that taking Ibuprofen eases both anxiety and depression. It's not a cure but it surprises me how much of a mental effect a mild analgesic has.
I'd caution anyone making a link between depression and NSAIDs from that paper. Most of those people probably climbed out of depression because they specifically administered pain medication to subjects with osteoarthritis. Suddenly being rid of chronic pain can be liberating.
Rethinking this relationship is a major point of the original thread/article.