My favourite game from that era was Talisman- which is basically Dungeons and Dragons without the Dungeon Master. Or to put it another way, Dungeons and Dragons for lazy people.
I played Dungeons and Dragons too- but that's another story.
Further back- when I was a kid myself- the games we played en famille (on winter evenings) were Scrabble and Cluedo. The thing about those two- which locks them in place as classics- is that there's skill involved. I was quite a whizz at Cluedo- good at befoozling the opposition and making deductions from other players' moves. Games where it's all down to the fall of the dice soon become boring.
Ailz and I bought ourselves a Scrabble set last Christmas and gave it a bashing over the festive season. Perhaps we'll fetch it out again this winter.
There was/is a horrible game called The Game of Life, which is Snakes and Ladders reimagined (though imagination has nothing to do with it) as a turn upon the middle-class treadmill. Go to university, get a corporate job, have kids, upgrade your house, get wheeled into the crem (only without the bit about the crem). More like the Game Of Not Having A Life, really. How cruel (and borderline sinister) to have kids play at being middle-management when they could be being shoguns or super-sleuths or orc-fighting adventurers.
Do people (I mean young people- not oldies reliving their youth) still play board games- or has all the action moved into cyberspace?