Basically any show on PBS Kids. I used to watch back when Mister Rogers' Neighborhood aired regularly on it. Other shows I watched included Zoboomafoo (with the Kratt brothers!), Clifford, Arthur (was sad when I heard it'd aired its final new episode recently), Cyberchase, and Clifford's Puppy Days. My parents didn't have cable until I was a teenager, so I was pretty much raised on nothing but PBS Kids (as far as TV shows I could watch).
Another show I used to watch when I was really young, though, was Disney's House of Mouse on ABC Saturday Mornings. I was devastated when they stopped airing it. We didn't have a TV guide or anything, so, when it simply didn't come on one morning, it caught me by complete surprise. On a less sad note, I think I actually still have Snowed In at the House of Mouse on VHS.