(The reverse is not true, however. Some very great saints were not incorrupt; St. Therese of Liseux is a famous example. Someone actually told her during her life that she would be incorrupt after she died. She said, "Absolutely not" ... and she was right.)
Relics are venerated as a tangible connection to the saint and his life. This has been true since the earliest days of Christianity, when the liturgy was celebrated in the catacombs surrounded by the relics of the martyrs. To this day, a Catholic (or Orthodox) altar generally contains a relic of a saint.