I'm 19 and heavily involved in my university film-making society. The society president this year, and the one last year (who is still involved now), both study the subject and know what they're talking about. Last year we had a social to see The Godfather at a local cinema, anyone from West Yorkshire will have heard of it. The Hyde Park Picture House, it's basically an old 20's style cinema that was done up and kept for the community, and still shows films in the classic style. They have some Hollywood stuff there occasionally, but mostly they show recent arthouse and film festival stuff, and older classics (like The Godfather). They recently held the Leeds International Film Festival as one of the main venues for the event. Anyway, sadly I missed the film showing last year as I couldn't find the picture house until it was too late (ironically, this year I live round the corner and pass it every day on my way to university).
But I digress. In the society we discuss proper film and we've had various screenings, and every Monday hold a joint screening with Italian Society showing classic Italian arthouse films (the Italian Society president is also a member of our society). We saw Citizen Kane last week and although I knew the 'Rosebud' spoiler, I absolutely loved it. The film was amazing and has got me hooked on Orson Welles now. Yesterday we saw a screening of an Irish film called Once, a musical film shot on an extremely low budget (only about $150,000 - not sure what that is in £s right now...). Again, it was brilliant. I saw Garden State with my housemates, we rented the DVD. It's a Hollywood film but you wouldn't think it, it was also shot on a low budget (it stars Zach Braff who was JD in Scrubs, and is also his writing and directorial debut). All of these films are classics and are amzing. They're the exact same films that the kids the OP describes would hate. But they're all worth watching and all give something amazing to you. Fine, I like some of the Hollywood high-octane explosions and CGI filled schlock and stuff like that. But nothing compares to the low budget masterpieces or the classics of years gone by, or the beauty of arthouse cinema. That's what the youth of today fail to realise. That's what we need to teach them.