If you do a forum search for "parod" you'll get a list that will probably jog your memory (and maybe introduce you to some new gems).   I wouldn't say they're all true "parodies." Some are just funny songs set to familiar tunes, others have pretty much entirely new lyrics but with a few puns on the original lyrics thrown in, and still others really do parody both the lyrics and the concept of the parodied song.

Anyway, among the ones I think are the real treasures are:

"Would You Like To Play The Guitar" - Pat Donohue's parody of "Swingin' On A Star"

"The Eensy Weensy Spider" - a true parody of "The Mary Ellen Carter"

"The Murderous Toy" - takeoff on Paxton's "Marvelous Toy," of course.

and an oldie but goodie from the 1920s (I'm told):

"Georgie On The IRT" - parody of "Engine 143"