There are quite a few reported cases of SHC, I've included the more interesting ones here - if you'd like more information on the other cases I suggest you go to the Anomalies site.
October 1938
Maybelle Andrews was with her boyfriend dancing at a nightclub. Suddenly flames erupted from her back, chest and shoulders. Her boyfriend was severely burned trying to put the flames out. He said that at the time there were no other flames in the room anywhere and that they had come from Maybelle herself. Maybelle died of her injuries on the way to hospital
January 31st, 1959
Jack Larber who was a 72 year old patient at the Laguna Honda Home in San Francisco had his clothing catch fire a few minutes after being fed. His attendant was out of the room at the time it happened but attempted to put out the fire when returning back into the room. Mr. Larber died of 3rd degree burns on February 2nd 1959. No explanation was found for the fire - Mr Larber was a non-smoker.
December, 1959
An autoworker by the name of Billy Peterson was found dead in the front seat of his car in Pontiac, Michigan. At first it appeared that Peterson had attempted suicide for the exhaust pipe had been bent to lead into the car's front seat. However Peterson's body had third-degree burns on his back, legs and arms, his flesh was severely burnt but neither his clothing or the front seat were damaged. It was also noted that hairs on the charred portions of the body were not even singed. On the death certificate the cause was noted as carbon monoxide poisoning but the burns were ignored
December 1966
92 year old Dr. Joh Irving Bentley was last seen alive on the evening of December 4th, 1966 by friends visiting to say goodnight at about 9.00pm. The following morning Mr. Gosnell, a meter reader let himself into Mr Bentley's house to go to the basement to check the meter. Mr Gosnell had permission to enter Mr. Bentley's house because Mr Bentley had limited mobility and could only move about with the help of a walker. Once in the basement Mr Gosnell could smell a strange smell and then could see a light blue smoke. Worried, he went upstairs to investigate. Mr. Bentley's bedroom was filled with smoke and in the bathroom there lay the charred remains of Mr. Bentley. All that was left of the old man was the lower half of his right leg with his slipper still on it. The rubber stoppers on his walker which lay beside his remains were still intact and the bathtub was hardly scorched. Gosnell ran for help. It was first thought that Mr. Bentley set himself on fire with his pipe, but it was soon discovered that his pipe was still on it's stand by the bed in his bedroom. The coroner noted his death was caused by asphyxiation and 90% burning of the body.
remains of Dr. Bentley
January 6th, 1980
Blackwood, Ebbw Vales, Wales - the police and forensic officers discovered a mans body burnt beyond recognition in his living room. The armchair that he was sitting in had hardly been damaged along with some nearby plastic objects. The fire that had killed the man had been so intense that it left a coating of vaporized flesh on the ceiling
October 1980
An airwoman by the name of Jenna Winchester burst into flames whilst sitting in a car next to a friend in Florida. Her friend saw yellow flames coming from Jenna and heard her scream "Get me out of here!" and saw her trying to beat out the flames with her bare hands. The car crashed into a telephone pole. Jenna survived the experience with 20% of her body covered in burns
24th March, 1997
Co Kerry, Irish Republic. 76 year old John O'Connor was found dead in his living room at Gortaleen by the community nurse who regularly visited him. Mr O'Connors charred remains were in a chair positioned some distance from his hearth. Only his head and upper torso along with his feet remained unburnt. There was little smoke damage to the room or furniture. The Local priest who attended the scene described it as "if somebody had poured petrol into his lap".