Hissy, hissy, little snakey,
Slither on the floor
You be good to Morfin
Or he'll nail you to the door.
-- Morfin Gaunt, translation from Parseltongue (HBP10)
Morfin Gaunt was the son of Marvolo Gaunt. He is first seen dressed in rags, his thick hair so matted with dirt the color was indistinguishable. He was missing several teeth, and his eyes, like those of his father and sister, looked in opposite directions. Morfin is a Parselmouth and a sociopath.
Morfin is summoned to a hearing by the Ministry for hexing a Muggle (Tom Riddle). When he resists he is arrested, convicted, and sentenced to 3 years at Azkaban (HBP10).
Years later, his nephew Tom Riddle paid him a visit. It was then that Tom learned that his father was a Muggle. Tom Stupefied Morfin, then went to the Riddle house and murdered his father and grandparents. Before leaving Little Hangleton, Tom stole the gold ring that was a Gaunt family heirloom. When questioned by the Ministry, Morfin confessed to the murders, so Tom must have also implanted false memories. Morfin died at Azkaban during his second incarceration (HBP17).
Morfin was the uncle of Tom Riddle who later became Lord Voldemort, through his sister, Merope Gaunt Riddle.
Parselmouth, keen on snakes
'Morfin' is possibly a homonym for the powerful drug Morphine, a highly addictive pain reliever. The word morphine, in turn, is rooted in the name 'Morpheus,' the Greek god of sleep and dreams.
We are not told when Morfin died. However, it seems from the text that Dumbledore spent only a few years trying to track down the details of Voldemort's past, starting from his conversation with Harry about the Diary, which would put Morfin's death in the early to mid 1990s.