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On the Late Show's first-ever episode, Monday, Aug. 30, 1993, Bill Murray helped Letterman mark his territory by spray-painting his desk with the word "DAVE." Murray would go on to become a frequent guest – often pulling memorable stunts during his appearances.
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On night two of the show, Robin Williams did what he did best – make people (in this case, Letterman and the not-pictured audience) laugh.
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Along with the actors, actresses, models, politicians and comedians, there have been plenty of musical visitors to the Late Show, too. Here, David Bowie performs in the show's early years.
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Letterman cracked up while interviewing a 34-year-old George Clooney, then the hot new star of ER.
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Demi Moore sported her buzzed-about shaved head (for her role in the film G.I. Jane) during a trip to the Ed Sullivan Theater to talk up another of her controversial flicks, Striptease.
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Italian actress Sophia Loren brought a little bit of home to the Ed Sullivan Theater in 1999, teaching Letterman how to make tiramisu onstage.
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Though generally light, the Late Show had its serious moments: Dan Rather, then the anchor of CBS Evening News, got choked up while discussing the Sept. 11, 2001, terrorist attacks.
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On this particular episode, everyone in the audience was a resident of Schoharie, New York, and the town's mayor read the nightly "Top 10" list. Nine years later, the village would pop up on Letterman's radar again; he helped fundraise for families there who'd been hit hard by 2011's Hurricane Irene.
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Synonymous with both Letterman and the Late
Show is the program's set at the Ed Sullivan Theater in Midtown Manhattan. In 2003, the New York Philharmonic performed on the building's roof.
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In preparation for Oprah Winfrey's first-ever Late Show visit, Letterman posed with a portrait of the two of them. At the 1995 Oscars, he'd made dud of an "Oprah, Uma, Uma, Oprah" joke, "introducing" the talk show hostess to Thurman, so Winfrey's 2005 appearance on his show was seen as a burying the hatchet of sorts (though she insisted there was never a feud).
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Letterman's hilariously awkward interview with Joaquin Phoenix went down as one of his weirdest. The nine-minute chat touched on Phoenix's hip-hop aspirations and an injury to Letterman's thumb, among other topics; it later came out that the whole thing was just promotion for Phoenix's bizarre pseudo-documentary, I'm Still Here.
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Two icons in one shot: the Ed Sullivan Theater, home to both
Letterman and the Late Show for more than 20 years, and Paul McCartney, who performed on the theater's marquee. McCartney and his band The Beatles made their U.S. debut in 1964 on the theater's hallowed stage.
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He's had many athletes on the show, but when New York Yankees first baseman Mark Teixeira stopped by, Letterman got in on the action himself: The two did a round of batting practice outside the theater on Broadway.
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Smooches all around! Dustin Hoffman planted one on Robert De Niro's head as they promoted their film Little Fockers together.
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Letterman and Cher have had their tense moments (back in the '80s, she called him an "asshole" on camera), but clearly, they came around on one another by 2013.
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The past and the future came together as Letterman snapped a selfie with Stephen Colbert, who's set to replace him as the host of the Late Show later this year.
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Taylor Swift's 1989 was one of the most talked-about albums of 2014 – and just a day after its release, she sang a few tracks on the Late Show.
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