I've recently gotten my girlfriend hooked on Trek by way of the original series on YouTube. Not on purpose; I was watching them and she started casually watching them with me. Imagine my delight when she started asking for more!
She's a complete sci-fi newbie and is drawn to the characters. She's especially taken a liking to Spock and McCoy and their 'gruff love' relationship.
Over the weekend, we had a movie marathon and tore through all six TOS movies. She recognizes The Wrath of Khan as the best of the bunch, said she had the most fun with The Voyage Home for the levity/humor (especially watching it directly after the relatively depressing preceding movie), and puts The Final Frontier as her next favorite. She actually let out a whimper during the scene with McCoy and his father, and laughed (in a good way) during the campfire scenes. She asked, after that movie, if the actors were friends in real life because she thought their relationship onscreen felt very genuine.
She dozed off during The Motionless Picture