I hate all of the toddler tunes albums I have. They always try to be too goofy, or just plain mess up the song. I’m not looking for trendy bands that did a one off toddler album (Although, I hear They Might Be Giants did one, and that might be good.) I know Pete Seeger has done some good stuff, so maybe he’ll have something, but I want traditional childrens music. No Disney characters or muppets.
This album was part of my childhood, though it might be aimed a little older than “toddler,” but it appears he has other albums that may well be the kind of thing you’re looking for.
This very day I added “Clap Your Hands” from TMBG’s No to my own playlist, just because it’s a cool song. I also enjoy lots of songs from Dog Train - especially “(Don’t Give Me That) Broccoli” and “I Need a Nap.” Laurie Berkner is good too, IMHO, and what I’ve seen of David Weinstone/Music for Aardvarks on Noggin is fun.
As a youngun, I loved Dr. Demento. Fish Heads. Pencil Neck Geek. King Tut. They’re Coming to Take Me Away Ha Ha.
Mmmm.
I’ll second Laurie Berkner. Also, even if you’re not Christian, you can pick through Veggie Tales and find some great stuff your toddler will love and the rest of the family will enjoy, too.
Sandra Boynton’s albums are great. Philadelphia Chickens, Rhinoceros Tap and Dog Train and Blue Moo. Dog Train and Blue Moo have songs by a number of prominent artists. You can check out samples on Amazon.
I came in to recommend Philadelphia Chickens.
My favorite kid’s album is a local dad and his wife and daughter who do kid-friendly hip-hop: Secret Agent 23 Skidoo. The website has some sample tracks on it; it’s really catchy stuff, IMO.
My grandkids love their “Dos Ninos” CD by this band:
They have gotten some airplay on Sirius/XM Kid’s Channel and do a lot of library shows aimed at small kiddies. I’ve been to a few and the kids love them.
Dr. Rock is a friend of mine, but I have no other connection to the band, so I’m assuming my posting the link is kosher.
I’ve never actually heard this music but I heard an interview with Dan Zanes and he seems to be trying to accomplish something similar to what you are looking for. The links to samples appear to be broken but if you do a search for his name on the linked site they come up.
http://www.danzanes.com/pages/dan_zanes.php
My two favorites are Lisa Redfern’s Hushabye, Lullaby and Greg Brown’s Bathtub Blues. (Sorry, no links, at work with no access to YT).
Bathtub Blues has songs that both toddlers and older children will enjoy. Some of it is silly, some sweet and some dark. The Lisa Redfern one is a good one to play during quiet time, as the title suggests.
I sang and danced to Free To be You And Me for most of my childhood.
Anything wrong with Sesame Street or Mr. Rogers? I keep Songs From The Street in my workday playlist, because that music is STILL the bomb.
Why limit it to “toddler tunes”? I found most of that stuff to be crap.
My kids were raised on Steely Dan, Paul Simon, The Beatles, and lots of other good music. I see no reason not to start with the good stuff early. YMMV.
Cathy Fink and Marcy Marxer have about a dozen albums, most (but not all) kids’ music. They are folkies from my old hometown, Takoma Park, MD, but have a national following.
You should look into Tom Chapin. We have In My Hometown and Mother Earth, and you can listen to samples of each of them there. The lyrics are for kids, and there are songs in different musical styles.
I’m really looking for traditional toddler tunes, like Old McDonald and Bingo and the like. She listens plenty of other music from me. I think the traditional toddler tunes are an important part of a child musical development. Children sing them in school. They tap them out on the piano. We sing them in the car.
I highly recommend anything by Ralph’s World. We like to say that he makes music for the children of parents who like good music. His live shows are a blast, too.
Here’s a good clip of his.
2nd Dan Zanes
Also check out Riders In The Sky Silver Jubilee
For the traditional kids’ music, I like Eric Nagler.
There’s also a John Lithgow album or two, and the Barenaked Ladies have done an album of music they wrote (more or less) for their own kids.
They Might Be Giants!
I saw them earlier today at the Union County Music Fest. They did a set with their kids’ stuff early and a regular show later. I love their kids’ stuff and they just came out with a new album.
Unauthorized Cinnamon–they played “Clap Your Hands.” Jealous? 
We have a few Justin Roberts albums, and I have to say that of all of the “kid music” I’ve heard out there (most of which is annoying crap), Justin Roberts is really enjoyable as an adult. He basically writes music that is interesting enough for an adult to listen to, but with themes and lyrics directed at kids. We’ve been to a couple of his concerts and they’re fun.
I have no problem playing the JR CD’s in the car on long trips.