at one time I reprimanded my dad for loving THE SIMPSONS and now I am a convert (I have seasons 1-9 on DVD). However, when I am at my brother’s house or my sister’s house, I don’t turn the show on unless the kids are in bed or out of the house, because there are some things that aren’t appropriate.
I’ve started bringing my FULL HOUSE DVDs with me when I visit my sister (my 7 year old niece LOVES to watch FULL HOUSE with me). And I bring Garfield and Friends or Rocky and Bullwinkle to watch with both my 7 year old niece & my soon to be 6 year old nephew.
I would say pay attention to the content in the show. Would you let your 5 year old watch the show FRIENDS which often had people: living together, having premarital sex, etc? (No, I never watched the show, but I do know about the content).
I miss the old family shows - ABC used to have TGIF with several good family shows. Now they have Grey’s Anatomy reruns on Fridays

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I think shows like Extreme Makeover would be okay for kids to watch - especially the episodes where they help families that have been devastated by disasters, the sudden death of a family member caused setbacks , or that don’t have a nice house to live in (like its full of mold, cracks in the foundation, etc).
7th Heaven is a show I’d recommend as they have dealt with a LOT of issues over the past 11 seasons: Suicide, Teen Pregnancy, STD scares, etc. And when they dealt with teen pregnancies, abortion wasNEVER an option they scream out. Probably because the father was a non denominational Protestant minister and they wanted to keep the show wholesome.