I think it's hard to separate "you should see this [because it's technically/artistically fantastic]" and "you should see this [because everyone else has so it's part of some wider body of knowledge now (FVSO everyone else)]" and "you should see this [because it will speak to you specifically, Janet, at this point in time and space]" and "you should see this [because I think it's a good way to spend two hours]".

That said, I think I'd suggest: Casablanca, if only because it filters into so many other things, it's almost the equivalent of Shakespeare in intertextual terms now; Cinema Paradiso because it explains why (some) film lovers love film in the way they do [warning: subtitles]; Memento because it subverts narrative lines beautifully, it's very clever and quite gripping; Some Like It Hot for similar reasons to Casablanca and also because it's just genuinely funny; Amadeus because it's beautifully shot and orchestrated and an interesting story (Schaffer text gives it a headstart too); Monsters Inc. because it will make you laugh and it's "cuddly"; 10 Things I Hate About You because Shakespeare adaptations work well with cute teens; Kiss Me Kate, Seven Brides For Seven Brothers, West Side Story, Singing In The Rain, Meet Me In St Louis, My Fair Lady because musicals are great fun for rainy Sunday afternoons - no one can be miserable with a musical (even one that ends in Bleak Despairing Death). Add some classic Ealing comedy, Clerks or Mallrats, some John Hughes (The Breakfast Club, perhaps)... I could go on for too long so I'll stop there.