I noticed this particularly while on holiday, as my travelling companion frequently tried to refer to films that she assumed I would have seen, and more and more I found myself apologising for being whatever the filmic equivalent of "poorly-read" is. ("Poorly-viewed" makes me think of frosted glass, and anyway, you know what I mean.) But it's something that happens quite often: people allude to films in the confident belief that they are accessing shared cultural reference points, and my only response is an unbecomingly blank look.
I'm also aware that often when I do watch films which everybody else has raved about, I feel as though I'm missing something. Obviously there are differences of taste, but with literature (and, in some genres, music) I feel as though I can make a critical judgement which satisfies me (I'm not particularly concerned whether other people's opinions differ) -- that is, I can say "I feel that I have read/heard and understood this and I am confident that my indifference to it or dislike of it is a matter of personal taste, rather than a sign that I am missing something which is central to appreciating it." (Goodness, that sounds arrogant. I don't mean it as such.)
Now I'm not really asking for recommendations of Wicked Cool Films You Like, because I've probably got enough of those to keep me going for the next 200 years, and unfortunately I'm only likely to live for another 60-odd of those. What I'm asking for is something slightly different: what films do you, O film-viewing people of my readership, regard as central to understanding film as a medium? Or, perhaps, which films are most central to the cultural consciousness of people in the English-speaking Western world? What films would you be horrified to discover that somebody in my cultural context hadn't seen?
 I'm specifying this because one of my reasons for asking is that film is an area where, at the risk of sounding melodramatic, I feel like an outsider in my own culture. I feel as though there are swathes of cultural referents which I am entirely missing because I'm so lacking in filmic knowledge. For other cultures I'm happier to accept that I will lack a lot of shared reference points.
Yes, everybody's answers are going to differ. I'm not really interested in producing a definitive list; rather just seeing what people suggest. I'm also interested to know reasons for your choices -- a list of films without any explanation will tell me nothing if I haven't seen them, and won't motivate me to see them.
Does this rambly and multifaceted question make any sense?