Arthritis was medical condition caused by joint inflammation, as a result of damage to the joints of the body.
In 2267, an exam by Doctor McCoy found advanced arthritis in Captain Kirk's shoulder after Kirk complained of shoulder pain. The arthritis was a byproduct of the accelerated aging that Kirk and several other members of the USS Enterprise were experiencing. (TOS: "The Deadly Years") By 2293, McCoy himself was suffering from mild arthritis, but this time from the natural progression of aging. (Star Trek VI: The Undiscovered Country)
In another case of hyperaccelerated aging, Doctor Pulaski experienced acute arthritic inflammation after being afflicted by aggressive antibodies on the Darwin Genetic Research Station in 2365. (TNG: "Unnatural Selection")
In yet another instance of artificially-accelerated aging in 2374, Commander Chakotay experienced chronic arthritis in his fingers in 2374 as the result of Srivani experiments. (VOY: "Scientific Method")
When The Doctor asked Lewis Zimmerman what the initial symptoms of his terminal illness were, in 2376, Zimmerman sarcastically told him "radical hair loss", before finally giving The Doctor his true symptoms of fatigue, nausea, and joint inflammation. (VOY: "Life Line")