Oddly enough there's very few bits of telly I remember watching with all of the family units. Classic 70s sitcoms like Fawlty Towers and Reggie Perrin mentioned above were one of them, but the vast majority of stuff I remember watching was documentaries, and the one the entire family was riveted by was one called Indelible Evidence, a really rather excellent docu-drama on murders that were solved through forensic science. Literally none of this light entertainment stuff was ever on show at home. The only time I ever saw a gameshow was either Catchphrase at one set of grandparents or Countdown at the others.
One thing I do remember is being banned from watching the A-Team when I was a kid because Boy George appeared in one episode and my dad was convinced it would turn me gay (that wasn't the term he used, and I didn't even understand what it meant until over a decade later), and then I was also banned from Horizon and anything Attenborough because of all their doom-mongering nonsense blather about so-called "climate change" (I think that was a fad of the 80s, don't think we've had anyone else go on about it since so just goes to show my dad's wisdom).
I think it was only when my dad was out that we got to watch Proper Telly. I have fond memories of watching the not-even-remotely-age-appropriate Edge of Darkness and Traffik covertly with my mum.