I am a Lord of the Rings thumping person willing to spout the goodness of nerdom to anyone that will listen. I could probably go full on door to door with it. Still, I suggest Star Wars, but I don't push it. I was thrilled when my younger sister (who disavows any association with geek) fell for Battlestar Galactica. BSG brought several people I know to the science fiction light, including those who "hate" sci-fi. I know, I know - BSG is a character driven show and by no means guarantees that those people will give say, Bladerunner a chance. A few of them did go on to watch Firefly though.
I've had better luck with using TV shows and movies to get people to open their minds a little. When I started devouring fantasy books with voracious greediness as a teen, I assumed everyone else would want to as well. If anyone I knew had a birthday and enjoyed to read, they got a copy of The Fellowship of the Ring or the like. I continued that through my early twenties, and I don't think any of the ten or so people that got the books gave them a chance. I doubt a page was read or even skimmed. Maybe J.R.R. Tolkien and Robert Jordan weren't the best starting places. A Vlad Taltos book by Steven Brust is still fantasy, but a lot more lighthearted and accessible. It might have been a better primer.
I still tend to find that most of my family and many I people I run into at the office or in everyday life have no interest in taking the leap from a real world to something more fantastical. They have a lot of preconceptions that no amount of me yammering on about the relevance of Middle Earth in literature is going to change. It's kinda like religion in that regard. My cousins have always thought it unspeakably not cool that I read comic books and like spaceships. Others, and I don't want to name names, think it's silly to waste energy reading about things that can never be real. I'm not kidding. It makes me sad sometimes because it feels like so much close-mindedness. Then again, they probably feel the same way when they talk about sports passionately and I just roll my eyes.