Don't mean to brag, but I can't remember being banned from watching any TV show or cartoon (well, cartoons anyway, I had no interest in live action shows then and few appeal to me now). When I was a kid in the lower grades of school (perhaps 1, 2, 3) I remember many of my friends and classmates not even being allowed to watch the Simpson's because that was considered pretty rude in the early 90's After all - there was no South Park or Family Guy back then. Those cartoons make the Simpson's seem pretty mild by today's standards My mother absolutely hated Ren & Stimpy, she told us numerous times that it was the most disgusting cartoon she's ever seen, but me and my brothers were a group of little boys - so we naturally loved it and my mother still let us watch it in spite of hating it herself (she wasn't fond of CatDog or Cow & Chicken either). South Park must have came out when I was like...still in the single-digits, so it's amazing I was allowed to watch that when NONE of my schoolfriends were (that sucked, I had no-one to talk to about it )
But you know what - my mother was confident enough in her ability to raise my brothers and I into decent kids and adults that she knew it was OK to just let us watch these controversial cartoons as long as we didn't repeat the language or behaviour demonstrated in there. And believe me, we did get in trouble if we tried, especially in public. But we were brought up to be better than that and realize that while it may be funny on TV - it's not appropriate in real life. That in itself is proof that good parenting can be a bigger influence on young kids than what they watch on TV (plus at that tender age I didn't understand most of the adult stuff in them anyway, half of all the jokes in South Park flew right over my head )
Anything anime related or young adult related. Young adult targeted stuff like Daria had cuss words in it, so they didn't like me watching that. Anime was just too...Japanese. It didn't make a lick of sense to them. They were okay with me watching it, but they made such a fuss over it that I never felt comfortable watching it in front of them. So I'd watch it, just not around them. So while these two things were taboo in the house hold...uproariously violent horror films and gay love stories were not, lmao. Me and mom watched romantic comedies featuring homosexual protagonists while me and dad watched zombies, vampires, ghosts, demons, and violence!! But no Daria or Tenchi. God help you if they find Daria or Tenchi!
I was never allowed to watch South Park which I think was pretty fair, although I would stay up secretly to watch it, getting caught a few times. They wouldn't let me watch any soaps either, which I was rather pleased about to be honest.
Other than "South Park" and "Family Guy", one cartoon show that my parents (particularly my father) didn't want me watching when I was younger was "The Ren & Stimpy Show" just because it was really gross for a kids show.
As a pre-teen, my mother didn't want me to view Futurama and Teen Titans, the former because of the dirty jokes (that I missed at a younger age) and the latter because of the action content. Which is terribly ironic because she watches CSI, NCIS etc. She hated the Simpsons, but I had my father to watch it with. They can't do a thing now, I'm old enough to select my own viewing pleasures.
Honestly, my parents really didn't care. My mom hated Sailor Moon tho. I guess she didn't like the style or something, I dunno. I used to love that show when I was a kid. I could care less about anime and stuff now. My parents and I watched The Simpsons together all the time! My dad even laughed at some things in South Park when he caught some of it. I'm thankful that my parents were cool about the stuff I watched on tv. Hell, my mom and I used to love watching horror movies!
This topic interests me because my mother had this supernatural power where she always walked into the worst possible moment of a TV show I'd be watching. I could be watching the most beautiful dramatic thought-provoking piece of art ever created. As soon as the rape scene comes on, my mother would walk in the room and be all like "What the hell are you watching!?"
To answer your question: South Park was a big one. So was Duckman. Pokemon sort of until I explained to my parents that the cute animals were not actually killing each other when they battled.