It could be a simple traffic stop, or a would-be victim who survives -- eventually, even the most meticulous of killers gets careless and gives cops the break they need to solve a case.
At least that's the hope.
As authorities hunt for more bodies in the thick brush along the South Shore's barrier beaches, where eight sets of human remains have been found since December, here's a look at how the law finally caught up to some of the region's most infamous serial killers.
David Berkowitz: 6 dead, one injured
A killer dubbed the Son of Sam terrorized New York City for a year, shooting and killing victims seemingly at random, most of them female, with a .44-caliber handgun.
In the early hours of July 31, 1977, he approached and shot a young couple parked in a car under a streetlight in Bensonhurst, Brooklyn. Robert Violante would lose sight in one eye but survive. Stacy Moskowitz died and became the killer's sixth and final victim.
Prior to that shooting, a woman had noticed a man, later identified as David Berkowitz, loitering in the neighborhood and said he appeared to have gotten a ticket on his cream-colored Ford Galaxie for being parked too close to a fire hydrant. She relayed the information to police.
"What broke that case was good old-fashioned police work," said retired NYPD Det. Sgt. Joe Coffey, one of the NYPD's lead investigators in the case.
During the summer of the Son of Sam terror, the police department was flooded with tips from the public, Coffey said. "It was a classic case of shoe-leather police work, going around door to door and really working on something," he said.
Some tips, of course, went nowhere. "We had many, many, many tips, from all walks of life, including cops giving up other cops, wives and girlfriends giving up their men," he said. Coffey called the vast majority of the tips "vendetta-type things."
Among the flood of misinformation, there were brief glimmers of the truth. Neighbors and a former co-worker told police about the troubling encounters with Berkowitz. "We did get three people who gave statements about Berkowitz during the investigation" before he was arrested, Coffey said. Berkowitz is serving six sentences of 25 years to life.
Among those credited with the arrest was NYPD Det. Edward Zigo of Lynbrook. He died in February at age 83.
Zigo's son, Edward Zigo III, said he and his sister were living with their father when he was assigned to the Son of Sam case. During the investigation, his father suddenly fell out of contact for 48 hours. Then came the phone call.
It was after the tickets were matched, but before the arrest.
"He said, 'I'm really sorry . . . I've just been so consumed by this. We are going through all these parking tickets . . . Ed, I think we've got him.' And I said 'What do you mean?' and he said, 'I think we've got our man.' "
Robert Shulman: Convicted in 5 killings
Postal worker Robert Shulman picked up women working as prostitutes in the Jamaica Avenue area of Hollis, Queens, and took them back to the room he rented in a Hicksville home. He would then kill, dismember and dispose of his victims.
The body of Kelly Sue Bunting, 28, of Hollis, was found in December 1993 in Melville. Like some of Shulman's other victims, Bunting's hands and left leg were missing and she'd died from blows to the head.
Several women who worked the same area in Queens led homicide detectives to Shulman's house and told them that he often picked them up in a blue Cadillac.
Shulman would be convicted of killing five women, two of them unidentified. He was sentenced to death, but that sentence was overturned by a 2004 Court of Appeals ruling that found part of the state's capital punishment law to be unconstitutional.
He was resentenced to life without parole, and at 52 years old, he died in prison in 2006 of an undisclosed ailment.
Joel Rifkin: Suspected in 17 killings, convicted in 9
Joel Rifkin had disposed of bodies all over the state: quite a few of them. But on June 28, 1993, the landscaper from East Meadow would try to dispose of his last one. The Mazda pickup truck that contained a body was missing a license plate.
State Police noticed and tried to pull Rifkin over. Trooper Sean Patrick Ruane testified at a court hearing in 1993 that Rifkin led police on a 25-minute chase at speeds that reached 90 mph before his truck slammed into a utility pole on Old Country Road in Mineola.
Rifkin surrendered and allowed himself to be handcuffed.
"At that point I started to notice a very strong odor coming from the vehicle itself," Ruane testified. "It smelled like decaying flesh."
In the back of the truck, under a plastic tarp, troopers found the body of 22-year-old Tiffany Bresciani. Rifkin would ultimately confess to killing 17 women between 1989 and 1993, many of them working as prostitutes, and be convicted of killing nine. He was sentenced to 203 years to life.
A trooper testified in 1993 that when Rifkin surrendered, he swore the plate was on his van when he left home and said, wryly, "It's always a 25-cent part."
Richard Angelo: Convicted in 4 killings
Nurse Richard Angelo injected his patients at Good Samaritan Hospital in West Islip with drugs that induced respiratory failure, then played the hero by being the first on the scene to resuscitate them.
Angelo may have been able to keep killing indefinitely were it not for a patient named Gerolamo Kucich, who came to Good Samaritan in 1987 to be treated for a heart attack.
Kucich would tell a court later that Angelo said, "This will make you feel better," before injecting something into his IV. "I couldn't move, I couldn't breathe," Kucich testified.
Somehow Kucich managed to call for help and was saved. The incident cast a spotlight on Angelo's activities.
Dr. Milton Beyers was a retired Good Samaritan internist asked by hospital officials to review Angelo's cases, and he spotted the patterns.
"I looked over the records, and it became obvious that all the patients had died or nearly died" under his care, Beyers said. "Just before the patients had problems, Angelo went in to attend to them."
Investigators exhumed dozens of bodies of people who had died suspiciously under his care. He was charged with six killings and convicted of four in 1989, and sentenced to 61 1/3 years in prison.
Angelo said after his arrest that he didn't intend to kill. He wanted to be a hero. "I wanted to create a situation where I would cause the patient to have some respiratory distress or some problem, and through my intervention or suggested intervention or whatever, come out looking like I knew what I was doing," he said at the time.
With Sophia Chang