Early in his 33-year reign as the king of late-night TV, David Letterman did a recurring skit called “Brush with Greatness.” Audience members would recount memorable celebrity encounters, like the flight service manager who said Barbra Streisand’s dog threw up on him, or the podiatrist who gleefully recalled how he almost hit Jerry Lewis with his car.

But those anecdotes pale compared with the life-changing encounters that some Mainers have had with Letterman himself.

There are people in Bangor, for instance, who are still basking in the glory of Letterman’s televised, headline-grabbing effort to get them to watch his show. Dan Cashman, of Brewer, became so fascinated with Letterman as a grade-schooler that he grew up to create, fund and host a statewide Letterman-style talk show. And nationally known Maine comedian Bob Marley counts his 1999 “Late Show with David Letterman” appearance as one of his big breaks, calling the laughs he got from Letterman “something I will never, ever forget.”

Call these moments a “Brush with Daveness.”

Letterman will host his last “Late Show” Wednesday on CBS, with his record as the longest-tenured late-night host in TV history secured (sorry, Johnny Carson). So while the entertainment writers continue to heap praise on Letterman for his wit and longevity, consider the Mainers who felt Letterman’s full comedic power in a very personal way.

Here are their stories:

PLEASE, BANGOR, WATCH MY SHOW

Cary Weston was a sophomore at Bangor High School, sitting in class one morning in 1987, when a classmate came in and said that Letterman had called his home the night before.

“No one believed him, because none of us stayed up that late,” said Weston, 42, a co-owner of the Sutherland Weston marketing agency in Bangor. “But it was true. And then it was all over the media. It kind of put Bangor on the map.”

On his Sept. 29, 1987, show, Letterman started reading the recent TV ratings for his “Late Night with David Letterman” on NBC, and saw his very lowest ratings were in Bangor. The number was less than 1 percent of all viewers.

So he decided to court Bangor viewers over the next several episodes. On some shows, Letterman showed maps of Bangor, or pictures of lumber or moose. He read names out of the Bangor phone book (thinking people would tune in to hear their own names) and even called Bangor residents at random to find out why they didn’t watch his show.

Newspapers and TV stations ran stories about the Bangor campaign. The New York Times even came to cover the story, quoting locals about how Bangor’s streets rolled up at 9:30 p.m., or how Bangor residents were going to start taping Letterman’s 12:30 a.m. shows and watch them sometime after sunrise.

Weston says Bangor folks did start watching Letterman after the campaign, and he and a whole generation became hooked on “Stupid Human Tricks” and Top Ten lists.

“Bangor wasn’t known, or we didn’t think it was known, so to see it in the national spotlight, and on the national TV news, because of Letterman, was pretty powerful,” Weston said.

A FAN IS BORN DURING SLEEPOVER

Dan Cashman of Brewer was 9 years old and having a sleepover in his parents’ basement when he and his friends decided to turn on the TV. His friends went back to roughhousing and joking while Cashman found himself transfixed by Letterman’s gap-toothed grin and razor-sharp wit.

“I just stopped paying attention to whatever was being said and concentrated on this wildly weird show,” said Cashman, 37, who runs Cashman Communications, a public relations firm. “I decided pretty soon after, that’s what I wanted to do.”

As a middle schooler, he sat behind a desk at home and pretended to interview people. While a freshman at the University of Maine, he convinced Bangor TV station WBGR to run the first version of his current statewide show, “The Nite Show with Danny Cashman.” After college, Cashman got married, had a child and started his business. But his dream of hosting his own Letterman-style show would not die.

About five years ago he resurrected “The Nite Show.” He hosts, books guests, writes jokes, sells ads and negotiates deals with local stations. Now “The Nite Show” is seen Saturday nights on commercial stations in all three of Maine’s TV markets: Portland, Bangor and Presque Isle. Guests have included Maine celebrities and politicians, and a few nationally known folks as well.

Cashman’s persona on the show is somewhat reserved, sometimes goofy, sometimes dry and witty.

“His (Letterman’s) influence is everywhere on our show. I try not to emulate him, but it’s hard,” Cashman said.

‘HE’S UP THERE RIGHT NOW, MARCIA’

Bob Marley was just eight years into his stand-up comedy career when he auditioned for Letterman’s “Late Show” in 1999. The day before his appearance, he stayed at a hotel across the street from the Ed Sullivan Theater and spent the night staring at Letterman’s name blaring at him in neon. He had never been on a network late show.

Marley’s first joke was about how a “very friendly” girl on a Manhattan street corner offered to spank him for $20, causing Marley to call his mother in Maine and say “Ma, you could make a lot of money down here.”

“I heard the laugh (from the crowd), and I heard Dave laughing behind me, which is something I will never, ever forget,” said Marley, 48, of Falmouth. “I’m waiting for the applause (to stop) and I can hear my parents in the front row, arguing, ‘He’s up there right now, Marcia, if you’d just shut it.’ ‘Why don’t you put a sock in your pie hole, Bob.'”

Marley said he was mortified for a moment that his parents would “derail” his five-minute spot. But no one other than Marley apparently heard them, and he continued with his act.

Since then, Marley has been on many of the big-name late shows, including ones hosted by Jay Leno, Jimmy Fallon and Craig Ferguson.

But he says the experience of going on Letterman’s show was unlike all others.

“At the end when (Letterman) shook my hand, I just stood there and stared at him, I was so star-struck,” Marley said. “It was like was I just watching him and didn’t know I was actually on the show. It was surreal.”