This article is from the of the muppets FAQ, by Craig Silverstein with numerous contributions by others.
http://home.nc.rr.com/muppetsongs/ http://members.tripod.com/Tiny_Dancer/sesame1.html http://www.punchandjewelry.com/legacy/html/lyrics_ind.htm
The first site has all sorts of Muppet and Sesame Street songs, including Rainbow Connection, It's Not Easy Being Green, Just One Person, the theme from "The Muppet Show," and more!
The second site, compiled by Tiny Dancer, has "Sesame Street" songs. Besides all the songs you'd expect (Rubber Duckie, "Sesame Street" theme), it has many Frequently Asked Lyrics: the Alligator King, Captain Vegetable, I Don't Want to Live on the Moon, We All Live In A Capital I, etc.
The third site has 232 songs (apparently all of them) from "Fraggle Rock."