"Kaeru no Uta," meaning "Frog's Song," is a Japanese children's song. It's neat because it's pretty easy to learn, and also because you can do rounds.
I don't know of any other songs that go to its tune, but essentially it's in a monotone, except the last syllable of every line, you raise your voice a bit.
Lyrics
Kaeru no uta ga
Kikoete kuru yo
Kuwa
Kuwa
Kuwa
Kuwa
Ke ke ke ke ke ke ke ke1
Kuwa kuwa kuwa
Translation
The frog's song
Come hear it (thanks to greyblue for the correction)
Ribbit ribbit ribbit (ad nauseam)
There's great fun to be had singing this with your friends, or in front of the uninitiated.
1 Can also be "kero kero kero kero," which also means (you guessed it) "ribbit ribbit ribbit."
ducksauce says: "Oh my. So Kaeru no Uta was the bane of my existence last year. My sensei was certifiably insane and we began and ended every class with this song. At one point, she made us make origami frogs and tulips. She then made us hold them while we swayed and sang the song. I'm glad this horrific memory has earned a place in cyberspace forever." I liked this anecdote enough to append it to my writeup.