So here are some of the more notable highlights from their exchange.
On his large family and working as a young kid in his father's bar:
"You have to deal with every jackass who walks in the door. Trust me, I need all the skills I learned growing up to do my job."
On his tan:
"Listen, I play golf, I ride a bike, I cut my own grass. My mother's dark complexion, so I'm a little darker. ... There's no tanning beds, no spray, never. Nothing."
On his last name:
"It's hard running for office when people can't say your name. You know, my name looks like Beener, Bonner, Boner. My first race for Congress, I was running against a guy named Kindness. But thank God my name wasn't Weiner."
"Boom. There you go," Leno said, as the drummer hit the snare drum.
"What took you guys so long?" he asked.
Does he think that the so-called "GOP infighting" is the worst it's ever been?
"Oh, no, well, yeah, maybe it is," he said as the crowd laughed. "It's bad. Listen, you know, the funny thing about the so-called infighting is that we agree on all the goals. We think Obamacare is bad for the country, we think we shouldn't spend more than what we bring in, we think the president's ignoring the laws. It's all a fight over tactics."
"Ted Cruz used to be my attorney a long time ago. A good guy. I don't always agree with him, but he's a good guy."
When Leno asked whether Republicans are to blame for the government shutdown:
"Yep," Boehner said.
"But when you have your job there's something you have to learn," he added later. "When I looked up, I saw my colleagues going this way. You learn that a leader without followers is simply a man taking a walk. So I said, 'If you want to go fight this fight, I'll go fight the fight with you.' But it was a very predictable disaster. So the sooner we got it over with the better. We were fighting for the right thing, but I just thought tactfully it wasn't the right thing to do."
The 2016 Republican presidential race?
"I'm not endorsing anyone. ... Jeb Bush is my friend and I frankly think he'd make a great president."
What about Chris Christie's problems?
"Doesn't appear he knew anything about it. ... This is not going to go away anytime soon. ... It may happen in New Jersey, but it doesn't happen in Ohio."
What do you think of Vladimir Putin?
"I just think he's a thug, I think he's treated his neighbors in a disrespectful way and frankly, I think the president ought to stand up to him and better protect America's interests and our allies, especially in Eastern Europe."
Ever think of running for president?
"No. ... Listen, I like to play golf. I like to cut my own grass. You know, I do drink red wine, I smoke cigarettes and I'm not giving that up to be president of the United States."
Notably, Boehner appeared as Leno's second guest, behind Matt LeBlanc, the star of the 1990s hit "Friends" and a show currently airing on Showtime. At one point LeBlanc and Leno joked that Boehner was playing second fiddle.
"He's third in line to the presidency, you're on a TV show," Leno said to LeBlanc.
Watch video of the segment here:
Updated and corrected 12:24 p.m.: The item has been updated to accurately reflect the last name of Boehner's first congressional opponent.