first the worst
"First the worst, second the best, third the dirty donkey." Dirty donkey also known as Hairy Princess. Obviously sung by people who weren't quite first, and taken unusually seriously by the person who was first, who in theory shouldn't have anything to prove to the person s/he just beat. Also used to punish the third place, who was often rewarded with a beating (or, in toilet related adventures, pissy trousers). The third person, however badly humbled, could take solace in the fact the he wasn't as bad as the person who came first, who was, after all, the worst.
written by Jo* Blyt*, Ni*k *ee*, approved by Log

fourth the golden eagle, fifth the witch, in the ditch, eating bread and treacle. This was pathetic, and made no sense to any of us. No-one gave a shit about being fourth or fifth to be honest.
written by Da*y *, approved by Log

First the worst / Second the best / Third the one with the hairy chest
Fourth the king / Fifth the queen / Sixth the one in the washing machine.
In this version, finishing third is even more desirable than second to boys, so any boy winning a race would stop just before the finish, and wrestle two of his opponents over the line before him. Girls unable to finish in the first two places would have to slow down and settle for fifth. The sixth position carried no real threat, however, as any cries of "you're the one in the washine machine" could be met with the unarguable comeback, "no, I'm not".
written by An*n , approved by Log

Third the Nerd the Golden Bird (?), Fourth the Dork, and we never bothered to get to fifth.

One might notice this doesn't even pretend to make sense.
written by Pa*l De*ton, approved by Susan

Alternative:

Fourth the angel, fifth the ghost, sixth the one who burnt the toast.

The implication here seems to be that not possessing rudimentary cooking skills is a fate worse than death.
written by excluded pupil, approved by Phil

In Ireland, the end bit goes:
Fourth the one with the golden hair / Fifth the one that God loves best
Not sure about sixth, but being fifth meant you got laughed at even more than the hairy-chested third place, generally including accusations of being a 'gay paedo'.
written by ca* cosg*ove, approved by Matt

In Yorkshire in the 70's, we managed to have awards for the first ten places.

First the worst
Second the best
Third the royal princess
Fourth the King
Fifth the Queen
Sixth the witch of Hallowe'en
Seventh the Executioner
Eighth the Dirty Donkey
Ninth the girl
Tenth the boy

There's such an impressively deflating failure of imagination in the ninth and tenth positions that you kind of feel like you're letting yourself down as you chant them.

"You're a boy."
written by an*nym*us *ser, approved by Log