There's a great Welsh one called "Dow hyfryd mis" which can be divided up in halves, quarters, eighths and sixteenths. If I can find it I'll post it.

Joan Mills, a great friend of Frankie Armstrong's, used to start voice workshops with this round as a vocal exercise.

There once was a man from Calcu-u-u-utta
Who had a most terrible stutter.
He said p-p-p-p-please
Pass the ch-ch-ch-ch-ch-cheese
And the bu-bu-bu, bu-bu
Bu-bu, b-bu-bu, bu-bu-bu-bu, bu-bu (pause)
Butter