As a kid, I learned a short version of this as a nursery rhyme, and only recently learned that there's more to it.

From The Nursery Rhymes of England By James Orchard Halliwell-Phillipps (which was published as part of "Early English Poetry, Ballads, and Popular Literature of the Middle Ages" by The Percy Society, 1841:

Old King Cole
Was a merry old soul,
And a merry old soul was he;
And he called for his pipe,
And he called for his glass,
And he called for his fiddlers three.
And every fiddler, he had a fine fiddle,
And a very fine fiddle had he;
"Tweedle dee, tweedle dee," said the fiddlers.
Oh there's none so rare,
As can compare,
With King Cole and his fiddlers three!

[Alternate versions:]

I.
Old King Coel
Was a merry old soul,
And a merry old soul was he;
Old King Coel,
He sat in his hole,
And he call'd for his fiddlers three, &c.

The first, he was an Irishman;
The second, he was a Scot;
The third, he was a Welshman;
And all were rogues, I wot.

The Irishman lov'd usquebaugh;
The Scot was drown'd in ale;
The Welshman had like to be chok'd by a mouse,
But he pull'd her out by the tail.

II.
Old King Coel
Was a merry old soul,
And a merry old soul was he;
Old King Coel,
He sat in his hole,
And he call'd for his pipers three.

The first, he was a miller;
The second, he was a weaver;
The third, he was a tailor;
And all were rogues together.

The miller, he stole corn;
The weaver, he stole yarn;
The little tailor stole broad-cloth,
To keep these three rogues warm.

The miller was drown'd in his dam;
The wearer was hung in his loom;
And the devil ran away with the little tailor,
With the broad-cloth under his arm.