Even when CBS's "Late Show with David Letterman" veers into awkward, uncomfortable territory for the guest -- as it often does -- Letterman never loses his cool. In fact, the opposite happens: The show only gets better. Now, after more than 30 years in the business, Letterman's mastered the art of pressing just the right buttons to ensure great TV. In honor of the 20th anniversary of his CBS show on August 29, we did the tough work of narrowing down our favorite 20 "Late Show" moments. 
Everyone knows that Bill Murray had the honor of being one of "Late Show's" first guests -- the actor is commemorating the occasion on the talk show Thursday -- but our favorite moment from the first "Late Show" episode involved Tom Brokaw. The veteran newsman showed up with a gag that some of Letterman's jokes were NBC's intellectual property, and took away his cue cards. 
In March 1994, Madonna severely tested Letterman's mettle in an exchange that's become a standout late night moment. Letterman introduced Madge as a top-selling pop star who'd slept with some of the biggest names in the industry, which prompted Madonna to go off a very profane deep end. At last count, somewhere around 13 F-bombs were dropped over the course of the interview. 
Any moment with legend Johnny Carson and legend-in-the-making Letterman was destined to be a classic, but Carson's appearance on the "Late Show" in May 1994 is the most memorable. The former "Tonight Show" host opted to make his last TV showing with Letterman, who appropriately handed over his desk chair to his idol. 
When Drew Barrymore showed up on "Letterman" in 1995, she came bearing gifts -- of a sort. The then-20-year-old actress was a ball of "good energy," and when talk turned to her interest in "nude performance dance," Letterman of course had to get a preview -- complete with flashing. It was his birthday, after all. 
Farrah Fawcett weathered accusations of being on drugs after her sit-down with Letterman in 1997. Ryan O'Neal later wrote in his book, "Both of Us," that Fawcett was trying to play the part of a "ditzy bunny," since she was promoting her Playboy spread. 
In January 2000, Letterman was put out of commission for a while as he underwent a quintuple bypass surgery. In true Letterman fashion, he made his grand return to thunderous applause accompanied by two adoring members of his medical team. "Wait until you hear what happened to me," he cracked at the top of his monologue. 
Letterman's first show after the September 11 attacks was an understandably subdued and emotional episode. The monologue was skipped in favor of honoring those lost in the attack. Dan Rather was one of the night's guests, and he memorably couldn't hold back tears as he recited "America the Beautiful." 
In the fall of 2002, Letterman showed his graciousness and tender heart when he dedicated an entire episode to the terminally ill Warren Zevon in a celebration of his music. The singer-songwriter passed away the following year. 
In March 2004, Courtney Love tried to pull off what Drew Barrymore had adorably done a decade earlier. Unfortunately, Love's would-be teasing reveal turned into a major -- and memorable -- fumble. 
After Johnny Carson died in January 2005, David Letterman paid tribute to him in the best way he knew: by turning over his entire monologue to the celebrated comedian and TV personality, composing it of jokes Carson had written. 
It had been 16 years since Oprah Winfrey last set foot on "Letterman" when she finally returned in December 2005. The episode of course brought in monster ratings, as it appeared that the two were making up. The irony was that neither truly knew -- or at least would admit on TV -- what caused their supposed "feud," or if there was ever a tiff in the first place. 
When you need to make a massive apology, it makes sense to turn to the well-respected Letterman to help you out. That's what "Seinfeld's" Michael Richards ended up doing in November 2006, with help from Letterman's guest of the night, Jerry Seinfeld. Richards, however, wasn't in the studio -- he made his apology via satellite after coming under fire for using the N-word during a tirade at a comedy club. "Awkward" doesn't begin to describe the appearance. 
Before Bill O'Reilly and David Letterman found a reason to high-five one another in 2011, they'd had a war of words while taping "Late Show" in 2006. The conversation was about the Iraq War, and the debate became so agitated that the light-hearted comments turned into terse insults. 
Paris Hilton braved seeing Letterman again in 2008 even after he upset her during her 2007 interview. The late night host grilled her about her jail time to the point that she said she was "sad" she'd even come on the show. The following year, Letterman acknowledged how tough he'd been on the celebutante and made nice. 
After initially trying to skip out on Letterman's show in 2008, John McCain finally made it into the hot seat that October. The politician was faced with chatting up a man who roasted him for his cancellation in an earlier monologue. Both moments were deliciously squirmy TV. 
Watching Joaquin Phoenix appear on "Letterman" in 2009 was like watching a train wreck -- it was so hard to watch, but you just couldn't look away. Phoenix had drastically altered his appearance and behaved strangely, as Letterman tried to figure out how to navigate the puzzle before him. It was all an act, though, and Phoenix returned to the show in 2010 to apologize. 
In October 2009, Letterman made a stunning admission live on the air when he told his audience that he'd had sexual relationships with female members of his staff, and that someone had been attempting to blackmail him as a result. The following Monday, he used his show to offer a "heartfelt" apology to his wife and to his female staffers. 
Richard Simmons and David Letterman have a wonderfully antagonistic friendship, and out of the many times the fitness king has appeared on the program, it's hard to pick a favorite. This moment from 2009, when Simmons and Letterman bickered over how to use a food steamer just before it burst into flames, is the kind of late night gold that other hosts dream about. 
Letterman isn't above poking some friendly fun at his rival, Jay Leno, and in the disastrous NBC late night wars of 2010, Letterman kicked it up a notch. But, we assume, it was all in good fun -- Letterman still joined Oprah Winfrey and Leno in a "Late Show" promo during the Super Bowl that year, an ad that was said to be Letterman's idea. 
Prior to her court-mandated stint in rehab, Lindsay Lohan gave an emotional but also surprisingly endearing and transparent interview. Letterman, of course, didn't take the easy route and asked pointed, frank questions. Although he led her down a road that ended in tears, the host commended Lohan when it was done: "We never thought we'd see you again, honestly, because of the jokes and stuff," he told her. "But you have enough spine, enough sense of yourself, enough poise to come out here and talk to me." 
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