Very early in Peter Parker's career as Spider-Man he started out as a wrestler. One night after a match Spider-Man witnessed a man robbing the stadium but did nothing to stop him. After Peter came home later that night he saw police at his house and one of the officers told him that his Uncle Ben had been killed at that they had his murderer cornored in an abandoned warehouse. As Spider-Man, Peter arrived at the warehouse and captured his Uncle Ben's killer only to learn that it was the same man that he let escape earlier at the arena. The burglar was then arrested and Spider-Man learned that with great power comes great responsibility.
In the comics
While in prison the burglar learned that his cell mate, "Dutch" Malone", which was an infamous 1930's gangster, had hidden treasure in a house in Forest Hills.
When the burglar got out of prison he went to the house to search for the treasure. The house was now owned by May and Ben Parker. When Ben attempted to stop the burglar, the burglar shot and killed Ben. Spider-Man later brought him to justice.
Years later the burglar escaped prison and kidnapped May and threatened to kill her if she didn't reveal where Malone's treasure was. As Spider-Man arrived the burglar died of sheer terror of the sight of the wall crawler.
In Spider-Man 3 the buglar's name was revealed to be Dennis Carradine. It was also revealed in Spider-Man 3 that Carradine didn't kill Ben Parker. Instead Ben Parker was killed by Flint Marko who years later became the Sandman.
In video games
In the 2002 Spider-Man video game (which was based on the first Spider-Man movie) the burglar's name was Spike.
In the television series, The Spectacular Spider-Man, the burglar was Walter Hardy. He is the father of Felicia Hardy a.k.a. Black Cat. Early in his career as a cat burglar Walter never carried a gun but as he got older he also got slower and started to carry a gun. One night after robbing the Parker house, Walter accidentally shot and killed Ben Parker. Years later Black Cat attempted to free Walter from prison but he chose to stay in prison to pay for his sins.