OK, I'll just dump the whole file on you, trying to edit out the things I know have been covered:

Rattlesnake Dance by Jim Arnosky has music inside the front flap.
The children LOVE this book.

Traditional ones like "Old MacDonald"

"Over in the Meadow"

ones that use traditional tunes but change the words like "Seals on the Bus"

There Was an Old Lady Who Swallowed a Fly;

There Was an Old Woman Who Swallowed a Pie;

This Old Man (the counting song);

Little White Duck;

To Market, To Market;

Itsy Bitsy Spider.

Paxton's Engelbert the Elephant   (and others)

David Mallett's Inch by Inch

Bill Staines' All God's Critters Got a Place in the Choir

The E Raffi version of just about anything.

Go Tell Aunt Rhody;

Reynolds'Morningtown Ride;

picture book versions of 12 Days of Christmas;

Langstaff's version of Oh A Hunting we will Go;

Spier's Erie Canal;

picture book versions of Star Spangled Banner
and America the Beautiful (j811.5, Bates)

Sitting Down to Eat by Harley

Mockingbird by Ahlberg (a new version of the traditional song)

anything by Iza Trapani (especially Shoo Fly)

       The Green Grass Grows All Around by Hoffman
      
Miss Mary Mack by Hoberman
      
Froggy Went A Courting (I like the Conover Version for
             pictures, but use my own version of the song)
      
Animal Boogie by Harter
      
The Farmer in the Dell (I like the O'Brien version)

Hurd, Mama Don't Allow

singing nursery rhymes to the music of "Yankee Doodle," the theme from
the TV show, "Gilligan's Island" and (pardon me for this one,)
"Ninety nine bottles of beer on the wall."   


There Ain't No Bugs On Me by Jerry Garcia, et al (Be warned the last verse does have HELL instead of HECK)

This Land Is Your Land by Woody Guthrie
T
hree Blind Mice by John W. Ivimy

A Farmyard Song by Christopher Manson

To Market To Market by Anne Miranda