Cancer was a disease in which cells divided uncontrollably. It was one of the deadliest diseases on Earth until scientist Pyong Ko discovered the genetic sequence for inhibiting the growth of cancer cells. (VOY: "Fury")
It has been repeatedly mentioned that disease on Earth was eliminated within 50 years of First Contact. This is one of the few examples where specific information is given.
Bernadette Fuller, a colonist on Terra Nova colony was diagnosed with lung cancer, though it was easily treatable with Enterprise's medical equipment. (ENT: "Terra Nova")
Emory Erickson was told of rumors that the transporter could cause brain cancer in its users. (ENT: "Daedalus")
Cancer can be found in the form of a tumorous growth. Ptera, a Vhnori, had a cancerous tumor on her brain stem in 2371 until it was removed by The Doctor on the USS Voyager. (VOY: "Emanations")