My parents didn't let me watch Cartoon Network for ages. By the time I was on, Looney Toons was in its last years. I also remember when the shows Cartoon Network had started shifting over to Boomerang- I had watched Flintstones/Jetsons, Dexters Lab, Johhny Bravo (not that I got it), etc. I liked Edd, Ed n Eddy, but I'd say most of what came after that I despised. There were quite a few deservedly short-lived series while they reworked their image.
Anyway, for reasons I cannot imagine, before I was allowed to watch Cartoon Network, I could watch all the Speed Racer (which I remember for a while at least having a life in the channel-themed interludes on CN, though I don't think I was awake when they aired it) I wanted. Which is weird because it had, particularly taboo outside of Looney Toons, guns. I also watched Pokemon for a little while, but I missed Pokemon The Movie 2000 and immediately stopped caring.
And they weren't cartoons, but probably my two absolute favorite childhood shows were Bill Nye and Junkyard Wars. I loved seeing how stuff worked (I was one of those kids that asked "why" all the time). Oh, and plenty of Magic School Bus.
I was a little too young to enjoy Courage the Cowardly Dog, and I particularly disliked Samurai Jack (I'm of the opinion that I missed out, looking back) for its emphasis on unusual art style. Lesee... Power Puff Girls I didn't watch. Because it was girly. And I thought that Cow and Chicken was just plain stupid, even at a young age. I also didn't watch much of what was on the disney or nickelodeon channels, for little particular reason. I ended up watching Spongebob when I was 13 or so. Oh, and I had made up my mind not to watch superhero shows for some reason, I'm not sure. At some point I saw the Batman cartoon (which ever era you remember as the 'good one', that was probably it) at a friends house on DVD, and was convinced otherwise.
I also really, really hate the Batman/Iron man shows that are out now. They bear numerous traits that I lack a better word for than "Godawful". And I'm sure it's not just because I'm not younger either.