First and foremost, unless you teach kindergarten or have small children, listening to nursery rhymes (regardless of language) is like dragging nails on a chalkboard. Even then, it can be a cruel form of punishment. For only the brave, continue reading.
The first one that comes to mind for me is 곰 세 마리가 (Three Bears). Here's a blog entry that seems to dissect the song entirely. I'm sure anyone who watched 풀하우스 remembers it fondly.
내 동생 is made from pure sugar and should be considered mandatory for all kids. Here's a great flash animation.
동, 동, 동대문 is a twist on London Bridge is Falling Down.
At 3:52 there's a cute game known in English as the "Rose of Sharon" (no relation to the epic song from everyone's favorite metal band). The game is more like Red Light Green Light.
And, for the dog days of summer, straight from the forum, here's one with snowmen. Not so much appreciated now but maybe in a few months.
Rooraa, a fellow KC101 student, started this thread in the forum about a bunch of different children's song that is a pretty good starting point for the Korean Happy Birthday song, Catch the Mouse, and Polliwag.
Head Shoulders Knees and Toes is pretty much directly translated into Korean. Proof. Note: the gaudy singing is fairly standard for these types of songs.
And who could leave out the Telephone Song? Whether it was intentional or not, this video will make you laugh.
I gotta say that I'm a bit jealous. I mean, the majority of songs from my childhood consisted of church songs, motown, and Elvis Presley eight tracks. I think the only nursery rhyme game that I played was probably Duck Duck Goose.
As far as the quality of the tapes/CDs/mp3s of typical Korean children's music - it's abysmal. I don't know, maybe I just have run into
If you don't listen to any other Korean children's song, you owe it to yourself to hear....no, see this song. It's a little ditty about carrots.
For more on the subject (kid music, not carrots), here's a nice site with a few songs with English/Korean lyrics.