A few weeks ago I watched "A new hope" with my 13yo daughter, we both loved it. Of course the effects didn't age well, but the story and acting is as strong as it used to be. I'm going to watch "The empire strikes back" with her soon and have to be careful not to spoil the "I am your father" reveal. Though I admit she's not very typical - we're both Whovians ("number one fans", so to speak;-)), so she's accustomed to story, writing and acting being way more important than SFX (which is IMHO the correct attitude, at least most of the time).
I really hope that she'll find some fellow geeks soon.
Also, in my current team at work I used to be the only one who watched (and read) "The Princess Bride". Now one coworker also watched it, and one day we're going to watch it together with the whole team. I think many people nowadays know it only from memes, which is sad - it's a great movie.