The first time people hear about Couchsurfing.com -- an online community where users volunteer to host visitors to their city, and travelers can send requests to specific hosts asking to stay at their house –– their honest reaction is not always positive. When I say that I'm a host, people ask, "Aren't you worried about people stealing your stuff?" From my conversations with female travelers, it sounded like practically everyone asked them, "Are you sure it's safe staying with a guy from the Internet that you've never met before?" (Most female travelers are in their mid-twenties and quite a few of them don't even tell their parents what they're doing.)
On my side, I can say that I've hosted hundreds of people over the last five years. (I don't constantly have guests, but in the summer when the number of people looking for housing is the highest, I've sometimes hosted five people at a time in the living room. I make sure people know what they're getting into when I invite them!) As far as I can tell, I've never had anything stolen. In fact, I've never really had a bad experience at all, although that's at least partly due to the fact that I screen people's requests pretty carefully. The number one red flag for me is when someone's profile says that they live in Seattle (where I live), and their post says "I just need a place to crash for a couple of days..." That usually means they got kicked out of their current living space (whether for lack of rent payment or due to some bigger problem), and that's not something I want to get involved in. (On the other hand, if they just moved to the city and they need a place to stay for a week before their house or apartment becomes available, that's different and I've hosted those people before.)
But while I've never had a bad experience myself, I've hosted a lot of female travelers who sometimes travel alone, and they've made two points about their overall experiences pretty consistently. First, almost none of them have ever felt like they were truly in an unsafe situation where they actually felt threatened. Second, though, most of them have said that about one out of every five or ten times that they're staying alone with a male host, something happens to make them feel uncomfortable. These incidents, in turn, fell into two categories: (1) the guy would ask on the last night of their stay, "So, uh, want to make out?" the girl would say "Uh, NO!" and that would hang uncomfortably in the air for the rest of the night; or (2) the guy didn't do anything that crude, but over the course of them staying together, the woman sensed that the guy started falling for her, and she didn't feel the same way about him. (Once in a while, of course, she does feel the same way, and I've also heard some stories about relationships that started this way.)
If it still feels like too much to dive into for the first time, you can always sign up as a Couchsurfing member simply to meet travelers to your city without hosting them, or to meet other hosts living in your city. Talk to people about their experiences traveling and hosting, and find out the pros and cons. Many people are surprised to hear that a community like Couchsurfing is able to work at all, but clearly for many of its passionate longtime users, it has worked out great for them.