As Letterman mixed wisecracks with contrition, he said his wife, Regina Lasko, had been "horribly hurt by my behavior" and stated flat-out that those affairs "are in the past."
The CBS late-night host vowed during Monday's show to repair his relationship with his wife, whom he married in March after a years-long courtship.
"Let me tell you folks, I got my work cut out for me," he said ruefully.
As Letterman faces future shows, how he deals with his messy situation could prove significant and, ironically, it could clinch his recent ratings victory in late-night TV.
Monday's show was the first Letterman had taped since Thursday, when he disclosed that he had had sexual relationships with women who worked for him and said that he had been the victim of a $2 million blackmail threat.
While Lettermen laced his show with references to the scandal, only one other late- night host, Craig Ferguson, made any reference to it in his show. Jay Leno, Jimmy Kimmel and NBC's "Saturday Night Live" had all made jokes in earlier shows, but everyone but Ferguson avoided the topic on their Monday night and Tuesday morning shows.
As host of the "Late Late Show," Ferguson follows Letterman's "Late Show." Letterman also is his boss, since Letterman's production company, Worldwide Pants Inc., produces the "Late Late Show."
"The person you work for, the person you admire and respect, is caught in an embarrassing situation," said Ferguson. "And your job is to be funny about that, whilst trying to keep your own job."
"So this is my last show," he joked.
Ferguson did make light of the situation, joking that it had now been revealed how he got the job in the first place.
But Ferguson defended Letterman, calling him "the king of late-night television."
"If we are now holding late-night talk-show hosts to the same moral accountability as we hold politicians or clergymen, I'm out," said Ferguson. "I'm gone."
On the "Late Show," Letterman noted the cool fall weather, reporting, "It's chilly outside my house; chilly INSIDE my house."
Then he cautioned the audience, "This is only phase one of the scandal. Phase two: Next week I go on 'Oprah' and sob."
A bit later, guest Steve Martin gave Letterman his kidding consolation: "It proves that you're a human being. And we weren't really that sure before."
Martin Short, making an unannounced appearance, playfully plopped himself in Martin's lap.
"You spend one more minute on his lap, you're gonna get blackmailed," Letterman quipped.
During the hour, Letterman apologized to his staff, which, he said, had been subjected to "being browbeaten and humiliated" by reporters since his revelations.
"My thanks to the staff for, once again, putting up with something stupid I've gotten myself involved in," he said.
Letterman, 62, began dating Lasko in 1986, and they have a son, Harry, who was born in November 2003. All the affairs took place before Letterman's marriage, said Tom Keaney, spokesman for Letterman's production company.
Letterman arrived on stage Monday to applause and cheers from his studio audience. After drinking it in, he grinned sheepishly and inquired, with a mock stammer, "Did your, did your weekend just fly by?"
After pausing for the audience's sympathetic laughter, he went on: "I mean, I'll be honest with you folks - right now, I would give anything to be hiking on the Appalachian Trail."
"I got into the car this morning," he added, "and the navigation lady wasn't speaking to me. Ouch."
In a more somber display, Letterman voiced his mea culpas. Regarding his wife, he said that, "If you hurt a person and it's your responsibility, you try to fix it."
Letterman has offered no specifics about how many women he had sex with.
But the CBS producer accused of blackmailing Letterman used pages from a former assistant's diary that described an affair with the "Late Show" host, a law enforcement official said Monday. The ex-assistant, Stephanie Birkitt, went to live with CBS News producer Robert Halderman, who found her diary describing her relationship with Letterman and used it to help blackmail him, the law enforcement official said Monday on the condition of anonymity because the investigation was ongoing.
Halderman, a producer for the true-crime show "48 Hours Mystery," pleaded not guilty last week to extortion charges.
The flood of attention on Letterman was inevitable, and the way he initially dealt with this maelstrom recalled an embarrassing dilemma for another star in 1995.
For a celebrity the caliber of Hugh Grant, publicity - including speculation of career suicide - was unavoidable when he was arrested with a prostitute on Hollywood's Sunset Strip. But then he retreated to NBC's "The Tonight Show" to try to explain.
Host Jay Leno wasted no time before asking an instant classic of a question: "What the hell were you thinking?!"
Grant's appearance provided him with some needed image rehab. It also vaulted ratings runner-up "Tonight" past Letterman's "Late Show," a leadership position Leno held through his retirement from late night earlier this year.
Since then, Letterman has reclaimed a ratings edge over new "Tonight" host Conan O'Brien.
And now he may have truly sealed the deal. Beloved by viewers and critics for decades, he has abruptly freshened the enduring Letterman brand and demonstrated he still can surprise even fans who thought they knew him well.
But it isn't the first time Letterman has shown finesse in managing a firestorm.
In June, he had a run-in with then Alaska Gov. Sarah Palin over jokes made at the expense of her teenage daughter. He emerged from a tumultuous few days of protests and demands for his dismissal with a ratings jolt. And thanks to the dumb-luck timing of the flap, he also handily upstaged his much-hyped NBC rival just as O'Brien was taking over as "Tonight" host.
Letterman apologized to Palin and her family in what became another one of his memorable performances. But he has never stopped making jokes at Palin's expense - including yet another apology to her on Monday's show, just for good measure.
Associated Press Entertainment Writer Jake Coyle contributed to this report.