I feel your pain.
I think that everybody should have seen the majority of the movies on the IMDB Top 250 list. I have just had a cursory look at this list, and apart from about 10 movies or so, I have seen all the top 100 and consider most of them worth watching. (Only very few of these are black and white, too).
I just had that experience, that I showed my kids (11&12) Jim Carey's "The Mask", and they laughed out loud when Jim Carey pointed his array of huge guns at the villains and drawled "So, Do you feel lucky, punks?" ... without knowing that this is a reference to another, rather classic, movie. (I could not even explain the reference to them, as Dirty Harry is possibly not exactly what is suggested for kids in that age group )
Some of my favourite films are on the list : Notorius, Strangers on a Train, Haichi, The Night Hunter, Sunset Blvd, Rebecca, Monthy Python & the Holy Grail, All About Eve, The Appartement, North by Northwest, Dial M for Murder…………….