A song by The Beatles. This is, by now, a well known fact, but not noded:

The melody came to Paul McCartney in a dream. He woke up and plunked it out on a piano by his bed. He thought to himself "Why, that's a nice tune..." And he first went to John Lennon to ask him if he heard it, then to George Martin (The Beatles' producer) and asked him. They both responded saying they didn't know it.

After about a week, he decided it must be his.
The original lyrics went something like:

"Scrambled Eggs,
Oh my baby,
How I love your legs..."

and as you know, this was later changed to the lyrics we all know and love.

This is also the most-covered song in history, with some 2,500 versions of it...