In no particular order:
No!, Here Comes the ABC's, Here Comes the 1 2 3's, and
Here Comes Science by They Might Be Giants (best kids' stuff out there, seriously)
Pretty much anything by Dan Zanes (
House Party and
Catch That Train! especially)
Woody's 20 Grow Big Songs by Woody Guthrie, Arlo Guthrie and the Guthrie Family
There is a series called
For the Kids that has famous artists doing kid songs. Not all are great, but there are some fun ones we love.
Snacktime by Barenaked Ladies
is really good, but I think it's more for older kids. My six year-old tends to lose interest after a few songs. But there's a song about allergies that's totally worth it!
Woody's Roundup: A Rootin' Tootin' Collection of Woody's Favorite Songs, which is kind of the soundtrack to
Toy Story 2, is one of our favorites. It's all done by Riders in the Sky, and is a lot of fun!
Lisa Loeb did an album of camp songs (
Camp Lisa) that has some fun ones, but they can turn into earworms pretty quickly.
Old school Disney is another fun way to go. Soundtracks from
The Jungle Book,
The Aristocats, and
Lady and the Tramp are all excellent, and nowhere near as annoying or "pop-y" as the newer movies.
Okay, I could go on forever, so I'll stop.
ETA: While most of the above is technically kids' music, I think they really transcend it. If any of the music I've listed shows up on the iPod when I'm alone I'll still listen to it, which I'm guessing is sort of what you're looking for.