I've used Airbnb for a while now as a host, and I'm using it for the first time this weekend as a guest. I think it's a great system, and works really smoothly and efficiently from the host's perspective.
I really liked this article about Airbnb and other similar services.
http://www.wired.com/2014/04/trust-in-the-share-economy/ I especially appreciate the point about how the fact that money is transferred separately to the actual service means that you feel more of a connection with people. It's a lot more like having a friend of a friend stay over, and there's no awkward money conversations.
As for people over-staying their allotted time, we did have that happen once. They wanted to extend a three-day trip by a week, which was a little inconvenient. It's also a little hard to turn someone down when they're already in your house (at least if you try to avoid confrontation with strangers, like me). But they paid for the extra nights, which ended up making it worthwhile. I think normally people are travelling for a set amount of time so it's not an issue. Plus there's always the "oh but I have more guests coming after you" excuse.
I definitely recommend Airbnb as a easy and entertaining way to make money on the side!