1. Bill Murray is Dave’s first guest (1982)
For Letterman, Murray has dressed like Liberace, a Kentucky Derby jockey and a Renaissance fop. His first visit set the tone of the show when, after a long rant in which Murray decried the host’s “mind games,” Letterman responded, “Now that you’re well known, is it harder to be funny?”
2. Andy Kaufman and Jerry Lawler (1982)
In a hoax bit, comedian Kaufman got pro wrestler Lawler to slap him in the face as Letterman smirked behind the desk.
3. The suit of Alka-Seltzers (1984)
What some do for science, Dave did for comedy. With a snorkel and goggles in place, Dave was dunked into a fizzy experiment in laughter.
4. The Top 10 list debuts (1985)
“Heats.” “Rice.” “Moss.” These were the initial entries in the show’s first Top 10 list, “Things That Almost Rhyme With Peas.” Sometimes presented by politicians, celebrities, sports champions and everyday heroes, the lists–more than 4,600 of them–became Letterman’s signature bit.
5. Cher calls Dave an asshole (1986)
Letterman asked why it took Cher four years to agree to appear on the show: “Because I thought you were an asshole.”
6. Madonna won’t stop cursing (1994)
Letterman often had a flirty effect on female guests, causing many to leave filters at the door. Here, Madonna and Dave giggled and teased, discussing their underwear and making innuendos. Madonna sweetly told Dave he was a “sick f-ck.” Never has that term sounded quite so loving.
7. Drew Barrymore flashes Dave (1995)
In a ’90s version of Marilyn Monroe’s “Happy Birthday, Mr. President,” a braless Barrymore danced on Letterman’s desk.
8. Dave opens his heart (2000)
Discussing his heart surgery, the king of irony dropped the facade to pay tribute to the surgical team that saved his life.
9. Dave’s post-9/11 monologue (2001)
The first late-night host to return to TV, Letterman gave viewers real catharsis following a national tragedy. His eight-minute introduction was halting, honest and vulnerable, tapping into our collective fear and sadness. By the end, he also provided what we needed most: courage and hope.
10. Joaquin Phoenix rambles (2009)
After Phoenix’s incoherent babble, Letterman quipped, “Joaquin, I’m sorry you couldn’t be here tonight.”
–BY LARRY GETLEN
This appears in the May 25, 2015 issue of TIME.