The version I know is rather similar to the anonymous Guest shortly above me: learned from the Hash House Harriers. I had never heard of it having a tune. (Ya learn somethin' new ever' day.) We do it as a chant, call and response form, with each verse having it's characteristic, uh, motion/gesture.

Final verse:

[quietly]
Today is Sunday [fold hands in prayer]
       Today is Sunday
Sunday is a day of rest
       Sunday is a day of rest
but ...
[loudly again]
Saturday's a Hashin' day [running in place]
       Saturday's a Hashin' day
Friday is a f**king day [I'm sure you can imagine the 'motions' that go with this one]
       Friday is a f**king day
Thursday is a drinkin' day [take a swig of beer, causing a slight pause in the song]
       Thursday is a drinkin' day
Wednesday is a hummmmmm day [during the word "hum", hold two fingers vertically, spread slightly, over your lips]
       Wednesday is a hummmmmm day [Some women respond to this and to every succeeding line with "EVERY day is Wednesday!"]
Tuesday is two-finger day [demonstrate what you might do with those two fingers]
       Tuesday is two-finger day [ The ruder of the Hashers will respond, especially during the later verses, that "Tuesday is a fistin' day"]
And Monday is a wankin' day [for the Americans who might not know this British slang, it refers to male auto-eroticism; the motion should be obvious]
       Monday is a wankin' day
IS EVERYBODY HAPPY?
       YOU BETCHER @$$ WE ARE!
[ALL] Toodle-ee doot-d'-doot-d'-doot
Toodle-ee doot-d'-doot-d'-doot [Everyone puts one finger on the very top of their head and twirls slowly once; imitate a music-box ballerina]

BB,
NightWing