My DD14 (last summer, she's 15 now) was / is / probably for ever will be a complete ride chicken. I was too at her age, but I've gotten a good bit better over the years.
Over the course of our first two trips to Disney World, we managed to drag her on quite a few rides that she wasn't too sure about. Out of them all, the only one she went back on a second time was Soarin'. We took her on BTMRR, she grabbed hold of my side so tightly I had a bruise for two days after the ride. She had a COW on Splash Mountain, freaked out on Test Track, will NEVER go on Pirates of the Caribbean again for as long as she lives, and couldn't be convinced to even try the ride in Norway. She chickened out of the weenie side of Mission Space, cried all the way through Star Tours (what's so bad about that ride

), refused to try Kali River Rapids, and don't dare to even mention Space Mountain, TOT, RnRR or Dinosaur near her
My take on it is this: She enjoys the rides that she does go on. I try to encourage her to try new things at least one time, but I don't push too hard. I know she doesn't like anything with a drop in it, so I don't push her on Kali, or the Maelstrom. Anything that she really appears to be afraid of riding, I just let it go. She can sit on a bench, have a drink, and enjoy some people watching down time while DW and I take DS on the rides that DD doesn't like. When we have the opportunity, we indulge her with some extra shopping time, or repeat rides that she does enjoy, like Small World, and Journey into Imagination.