Michael Finnegan is a traditional children's song, often referred to as a nursery rhyme, but more properly a campfire song. It's first appearance was in The Hackney Scout Song Book (Stacy & Son Ltd., 1921), and it has a long history of being a fun group song -- despite the challenge of memorizing the verses.
It is a rather repetitive song, but the modern covers by The Wiggles and the like have stripped it down to a just single verse to be repeated ad infinitum (n.b., Barney and Friends did not rate children's attention spans so low, giving us four verses). This is no doubt because the verses are silly and garbled, making it hard to learn, and all the more so since there is significant variation in the exact wording. Here are a random selection of some of the more popular verses:
There was an old man named Michael Finnegan,
He grew whiskers on his chin-ne-gan.
The wind came up and blew them in-again,
Poor old Michael Finnegan, begin again.
There was an old man named Michael Finnegan,
He went fishing with a pin-ne-gan.
Caught a fish but dropped it-in-again,
Poor old Michael Finnegan, begin again.
There was an old man named Michael Finnegan,
Climbed a tree and barked his shin-ne-gan.
Took off several yards of skin-ne-gan,
Poor old Michael Finnegan, begin again.
There was an old man named Michael Finnegan,
He kicked up an awful din-a-gin
Because they said he must not sing-a-gin
Poor old Michael Finnegan, begin again.
There was an old man named Michael Finnegan,
He grew fat and then grew thin-again,
Then he died and had to begin-again,
Poor old Michael Finnegan, begin again.
There was an old man named Michael Finnegan
Ate his dinner from a tin-again
Was so good he ate some more-again
Poor old Michael Finnegan, begin again.
There was an old man named Michael Finnegan
Heard this song and began to sing-again
Hurt my ears, so don’t begin again
And that’s the end of Michael Finnegan! Finnegan!
While there is significant variation and no rules, the song is often sung slowly at the start, speeding up through the verses, to finish in a rush. It has become traditional to mime walking around like an old man with a cane while singing; YMMV.