Link-heavy post, beware!
So, I'm a fan of Phineas and Ferb and Teen Titans and I can deal with iCarly or Wizards of Waverly Place right along with 8yo Abby. I liked Danny Phantom pretty well, ditto the Powerpuff Girls, and I think I like Samurai Jack more than she does.
Spongebob not so much. Johnny Test and the Fairly Oddparents yuck, and OMG - the horrifyingly-bad tripe that is Fred: the Movie. That last we will not let her watch again; in spite of the iCarly kids visiting Fred on the show and therefore tacitly endorsing it, this is not a show that is appropriate for my second-grader. And I have let the folks at Nickelodeon know how I feel about that.
As for Little Lizzy's shows, well, I'm so done with Busytown Mysteries. I can get behind her love of the Backyardigans and Sid the Science Kid and Blue's Clues and the new Bubbleguppies. I can tolerate Dora (even though she has NO INSIDE VOICE), Kai-Lan and her whiny friends, and Pinky Dinky Doo. I adore the Upside Down Show (although there are only 13 episodes available and they get really old).
You'll note that I don't mention Sesame Street. Really, with the exception of the holiday specials and a couple Elmo movies, this one's mine. I love me some Count von Count and Big Bird and company.
Movies are a different story. Miss Abby is into anime these days and finding some that's appropriate is sometimes a challenge (although we have quite a collection). She's just discovered Star Wars and we intend to introduce her to Indiana Jones soon. Oh, and Ghostbusters, inappropriate language and all; she saw that last week. And of course animated movies that are for everyone.
I'm really grateful Abby's grown into "real" movies. An adult can only manage so much Barbie and the Magic of Pegasus or The Adventures of Holly Hobbie before tooth decay sets in.