Dennis L. Rader, the BTK Killer, was caught when a letter he sent to the media was traced to his church, where he was president of the church council. He was linked to at least 10 murders in the Wichita, Kan., area.
Arthur Shawcross, who killed 11 women in the Rochester area, was captured when he went back to a dumpsite, where he had left one of the bodies, to relive his killing of a prostitute.
And Joseph G. Christopher, Buffalo's .22-caliber killer, was caught when an Army nurse in Georgia overheard him bragging about killing black men in Buffalo.
Some of the most notorious serial killers have been done in by their own mistakes -- often by their boldness, their desire to taunt authorities or even, some say, their desire to be caught.
As Rader wrote in one letter, "How many do I have to kill before I get my name in the paper or some national attention?"
All serial killers are different, all haunted by different demons.
But the arrests of Rader, Shawcross and Christopher raise an obvious question about the Buffalo area's latest serial criminal, the bike-path killer:
Could he be done in by his own hubris, by his desire to taunt authorities, or even by his desire for "some national attention?"
The bike-path killer's latest attack, the killing of Clarence resident Joan Diver on Sept. 29, provides one hint that he may have become bolder.
Investigators have DNA evidence that the killer was in Diver's SUV, and they suspect he moved it after killing her.
Maybe he got spooked and needed to drive away from the scene quickly, investigators say.
Or maybe he moved the vehicle to taunt authorities.
"The moving of the car could very possibly be a challenge to authorities or increasing boldness on his part," Amherst Assistant Police Chief John C. Askey said. "That's one of the many theories or ideas that investigators are exploring."
"It's definitely a possibility that he thinks he's smarter than we are," Erie County Undersheriff Richard T. Donovan said. "If that's true, hopefully he'll try to call some attention to himself."
Charles P. Ewing, a forensic psychologist and University at Buffalo law professor, agrees that the killer is taunting police.
"He's also opened a line of communication with the authorities," he added. "This is a guy who essentially got away with two murders and a host of rapes. Now he's put himself back in a situation where he could be apprehended."
Ewing said it's conceivable the killer may want to get caught. He may just want attention. Or he may want to open a dialogue with the authorities.
"He could be trying to communicate something to police, that 'I'm here. I'm back. Catch me if you can,' " he said.
Investigators also are struck by the fact that Diver went missing on the anniversary of the bike-path killer's first slaying, the Sept. 29, 1990, murder of Linda Yalem.
"Right now, the way this guy communicates with police is by killing," Ewing said. "He killed Joan Diver and left his calling card -- the DNA evidence and the anniversary date."
Rader, the BTK killer, was caught after he reopened his dialogue with the public.
The Kansas man had communicated with authorities during the early part of his killing spree but remained silent from 1979 until he wrote a letter to the Wichita Eagle in 2004. That marked a 25-year gap.
The bike-path killer hasn't gone that far, but authorities suspect he has collected some mementos from his killing spree.
"I think that he has memorialized, in his own way, each and every act that he has committed, whether he has collected newspaper articles or [television] tapes or taken something from the scenes," Erie County District Attorney Frank J. Clark said. "I think, in some way, he has cataloged these things like any collector would."
Clark thinks it's difficult for outsiders to use a logical thought process to determine what's going through the minds of serial killers who are so lacking in rational thought.
"But do I think there is a certain part of them that cries out for public recognition or acknowledgment?" Clark asked. "I think that's true."
Local authorities have one huge advantage that wasn't available to detectives tracking Rader, Shawcross and Christopher: They know the bike-path killer's DNA.
But that won't solve the crime unless the person's DNA winds up in some database that can match his genetic profile with the killer's.
"I think it's going to be like anything we do in police work, a combination of hard work, a slip-up on his part or a break in the case," Donovan said.
Notorious serial killers have been tracked down in a variety of ways:
*David Berkowitz, New York City's Son of Sam, was caught after receiving a parking ticket that detectives later determined was written near the time and place of one of his killings. Arrested outside his Yonkers apartment in 1977, Berkowitz reportedly told police, "What took you so long?"
*John Wayne Gacy, convicted of murdering 33 males in the 1970s, was tripped up when the mother of a boy he was scheduled to meet alerted police about the boy's disappearance. Detectives, aware of Gacy's criminal history, began watching him. Then, in one of those cases of serial-killer bravado, Gacy invited police into his home, where they were overcome by the stench of his victims' bodies.
*Jeffrey Dahmer was arrested in a more traditional way, after police spotted a man with a single handcuff on his wrist who had just escaped from Dahmer's Milwaukee residence in 1991.
The bike-path killer seems more organized and careful than that. But he has left his signature -- his DNA -- at the scene of most of his attacks.
Detectives know they can't count on a DNA match. So they have to rely on the old-fashioned kind of police work, returning to the painstaking task of investigating all the bike-path attacks.
Askey and other investigators discussed the four main focuses of the investigation into the bike-path killer's sexual attacks on 10 women dating back to 1986:
Investigation of the Joan Diver killing, which has been led by the Sheriff's Office.
Fielding and following up the approximately 1,000 tips investigators have received, sparked by local and national publicity about the case.
That includes trying to eliminate, through alibis or DNA, the strongest possible suspects.
One law enforcement official estimated that investigators have gotten DNA swabs from roughly half a dozen to a dozen men.
Adding extra patrols, including some on all-terrain vehicles, on local bike paths. "We've definitely increased our preventive patrols on several paths," Askey said.
Exploring all scientific avenues, with the FBI's help, including suspect profiling, the geographical patterns of the attacks and an updated composite sketch of the assailant.
Authorities have compiled a host of patterns and theories about the bike-path killer:
His attacks have become more violent. Sex with his victims may have become less of a motivating force for him. The dates of his attacks seem important to him. He may have had military training. And he appears to have above-average intelligence.
Investigators continue to believe that someone out there -- a loved one, friend or neighbor -- has suspicions about the killer.
No one knows whether the killer projects an image of an almost model citizen, such as Rader, or someone who's considered more of a loner or fringe member of society, such as Christopher or Shawcross.
"I would think there's a possibility that it would be someone who people thought was an upstanding community leader," Askey said. "But someone probably will have an indication that he had some problems."
A trio of serial killers
Their own mistakes led to their capture
Dennis L. Rader, the BTK Killer, used his church's computer to write to a newspaper bragging about killing 10 people in Kansas, leading to his arrest in 2005.
Arthur Shawcross was arrested in 1990 when he went back to the scene where he dumped one of his 11 Rochester-area victims. He's now serving a 250-year prison term.
Joseph G. Christopher, Buffalo's .22-caliber killer, was overheard bragging about one of the four murders he was convicted of committing. He died in prison in 1993 at age 37.