I've known a number of writers who are terrified to talk about their stories because they believed that someone would steal their idea. But to be honest, that isn't very likely. Everyone has ideas. Not very many people are out actively trying to steal new ones. I'm not saying it's impossible, it's just not likely to happen.
The idea for a book is the easiest part. Some ideas are better or more exciting than others, but it's only an idea. It's not until it's been executed that there's any real value to it. Now if you start posting entire books online, there is a chance they will be stolen. Not usually by someone looking to claim it as their own and make money off of it, though that has been known to happen, but more likely by people wanting to read something for free. Although I don't think people are as likely to download a stolen book as compared to music, it does happen.
Although I don't think someone is going to steal my ideas, I don't tend to talk about my stories while I'm writing them. An idea that I thought was great might end up sounding dumb when I try and talk about it with someone. This isn't necessarily anything to do with the merit of the idea, but more to do with my confidence in it and how well it's developed. There are a lot of reasons not to write a book, having talked about it too soon doesn't need to be one of them. Besides, so much can change during the writing process. The part of a story that I talk about one day might be completely gone by the next.
Idea's do get stolen, that's a fact of life. However, it's really unlikely that it will happen to the average writer. More likely it would happen to really popular authors who can turn their ideas into best selling novels as opposed to unknowns such as myself. Generally I talk about my stories as much as I feel comfortable, and usually only to real life friends. It's more likely they will get bored of my obsession rather then steal the idea.