Rambling Old Man Monologue

"We can't bust heads like we used to. But we have our ways. One trick is to tell stories that don't go anywhere. Like the time I caught the ferry to Shelbyville. I needed a new heel for m'shoe. So I decided to go to Morganville, which is what they called Shelbyville in those days. So I tied an onion to my belt, which was the style at the time. Now, to take the ferry cost a nickel, and in those days, nickels had pictures of bumblebees on 'em. 'Gimme five bees for a quarter,' you'd say. Now where was I... oh yeah. The important thing was that I had an onion tied to my belt, which was the style at the time. You couldn't get white onions, because of the war. The only thing you could get was those big yellow ones..."

—Abraham 'Grandpa' Simpson, The Simpsons, "Last Exit to Springfield"

The tendency of an old person, normally male, to go off on a long-winded rambling speech about no subject in particular at the drop of a hat. Somehow the old man never seems to actually get boring, though for some reason he has a hard time staying on topic, mixing in admonitions of today's youth with fond recollections of the past, anecdotes about fashion, detours into politics, and pretty much any other subject imaginable.

Related to But I Digress. Occasionally the result of the old guy being a Motor Mouth. Sometimes invoked intentionally by an old person who wants to hold the floor. Occasionally combined with elements of When I Was Your Age. Compare Grumpy Old Man, who usually only indulges in this trope when he's pissed off. An example can be found here.

There is definite Truth in Television here.

Examples of Rambling Old Man Monologue include:

Film

The Stranger from The Big Lebowski does this.
Early in Beetlejuice, Adam runs into his hardware store, saying hello to the old barber next door, who starts talking - when Adam leaves, the barber is still talking...

Literature

Mr. Wojakowski in Connie Willis' Passage has a tendency of rambling off into WWII stories when he should be talking about his Near-Death Experiences. Then again, his WWII stories are mostly made up...
Samuel Taylor Coleridge's The Rime of the Ancient Mariner is an example, from 1798. Making this Older Than Radio.
Likewise, Mark Twain's The Celebrated Jumping Frog of Calaveras County is made of this trope.
Dave Barry Slept Here says that people who lived through The Great Depression will spontaneously start talking about how hard conditions were back then until well after their listeners get bored.
The outdoor humorist Patrick McManus has discussed this trope in some of his short stories. And sometimes offered up straight-up examples of it.
Purdy in the Warrior Cats series. Fans love it, characters get annoyed by it.

Purdy: Do you ever miss hunting?
Mousefur: As much as you would miss talking if your tongue fell out!

One of these led to a CMOH in the Sten series, when the old guy spoke up in support of someone who'd rudely interrupted him to get the discussion back on its proper Matter of Life and Death track.

Live Action TV

Star Trek: The Next Generation: Captain Picard recalls a seminar where the elderly Dr. Fesbender went off one such speech. It was really quite hypnotic.
- (-notic notic notic notic)
Cliff does this sometimes in The Cosby Show.
In Game of Thrones Grand Maester Pycelle launches into a lengthy reminiscence about all the kings he's served. To make Petyr, who Roz is spying for, think he's going senile and declare his loyalty.

Video Games

EverQuest had an NPC called Old Man McKenzie. The official description of him is: "Old Man McKenzie, a frequent patron of the taverns in the Plane of Knowledge, thinks you adventurers have it too easy these days! Back in his day they didn't have all this fancy armor and magical weaponry, they relied on their wits and not a little luck to survive! Think you've got what it takes to survive in McKenzie's Gold era?"
Knights of the Old Republic: Jolee Bindo is accused of this a few times.
Wendy Oldbag from the Ace Attorney games does these so fast that they're sometimes unreadable.
The Legend of Zelda Majoras Mask: Listening to such an old lady ramble on (and then fall asleep as she does so) is a way to skip ahead in time if you don't have the Song of Double Time, though if you manage to stay awake and listen to the whole story, you earn two Pieces of Heart out of the ordeal.
In Anachronox, this is one of the party member's explicit abilities.
One sidequest in Paper Mario: The Thousand-Year Door required you to listen to one of these (from Petalburg's mayor, old man Kroop). The reward wasn't very good.
Old Man Andrew of Mega Man Zero lapses into this.

Webcomics

Order of the Stick #218 ends with an old man starting, and only finishing four strips later because he gets home.
Cyanide & Happiness has this.

Web Original

Weaponized in Naruto the Abridged Series, by the Hokage, with "Old Man Monologue Jutsu!"
In The Movie of Yu-Gi-Oh the Abridged Series, Yugi's grandpa launches into one of these that turns into a Long List.
- ...that continues after the credits, and reemerges in another special!

Western Animation

Abraham Simpson from The Simpsons is a master of these.
- "I've actually got an interesting story about that, although I guess it's not so much interesting as it is long...and boring..."
In Avatar: The Last Airbender, Iroh does this several times, as part of his Obfuscating Stupidity.
In Rugrats, Lou Pickles (Tommy's grandfather) often does this. He also seems to have a strange fixation on the number fifteen while telling these tales.
Played for humor and heavily lampshaded in Danny Phantom at the end of Doctor Disorders, where Tucker gets stuck staying in a hospital room with an old man explaining how many things they didn't have when he was growing up. All done in the most patronizing tone imaginable.
Grandpa Reg in Phineas and Ferb is prone to these. His not-so-old son, Phineas and Ferb's dad Laurence, seems to have inherited the tendency (although he's less likely to completely forget what he was talking about).
In an episode of Rocko's Modern Life, Grandpa Wolfe shuffled along with his walker along the sidewalk in front of Rocko's house, rambling on and on...right up through nightfall.