Hi Tim - we have used AirBnB on three occasions in cities/towns in Italy, and have never used other rental services. So my experience with sites for vacation rentals is limited. Nonetheless, my experience with the site and the accommodations has been positive enough, to make this the first and only site I check when planning for an urban stay in that country.
The site does have sort of a "Big Brother is watching you" effect : you can't swap any type of contact info with the accommodation (address, e-mail, telephone number), although you can, and are encouraged to, communicate with the host on any other subject.
However, I find that aside from this, everything else is quite user-friendly and functional, as others have mentioned. The info provided is quite comprehensive, and if it isn't, you can e-mail the owner for more details. The search filters are useful - anything from dates and general location to amenities and prices.
As Pauline says, reviews can be questionable, and indeed we do have a tendency to leave over-positive reviews. However, reading reviews is a discipline somewhere between psycho-analysis and the performing arts - the final interpretation is yours. It doesn't matter if you're booking a rental or buying a backpack : you can't afford not to read them, but their value has a limit. In the end, you'll have to trust your common sense and instincts, just remember that both are fallible.
I attach a lot of importance to the photos and the way the owner describes the place. Good and numerous photos (varied ones, not tens of photos of the same vase), plus a detailed and useful description, show that the owner is aware of what people are looking for, and the importance of getting this clearly out in the open.
If the owner mentions any slight negatives - and certainly if he mentions outright issues (noise, mattress on the floor, etc.) - that's a sign that he is honest and that he himself doesn't want the hassle of dealing with complaints.
Remember - it doesn't matter what others like, it's what you want or need. The place can have a great location, price, and free parking, but if you can't ignore a cramped shower, or an uncomfortable sofa-bed instead of a real bed, then the sum of the experience will be less than great.
Others have mentioned here and there that you have to pay much in advance, but I think that's not exact : if I remember correctly, the site "freezes" an amount on your card, but the actual payment is only done after the stay, after both sides have said they're satisfied. Also, each host has different cancellation policies, one of several policies allowed by the site - so check that you're not getting into anything that is problematic for you.
Another thing we've seen is that for us, it's better to use an accommodation that is not the owner's residence during the rest of the week or year. You can usually tell by the photos or the description, what is what. However, this is completely a subjective thing, and others may have positive experiences with this.
The fact that you, as a user, are also reviewed, is in my opinion a reasonable and fair policy, that adds an aspect of responsibility and honesty to the model.
I like AirBnB. They have shaken the industry and provided tourists with a good alternative. It's true that one of the negative outcomes of their success has been a big rise in short-term rentals in residential parts of popular towns and cities, sometimes to the (great) anger of the locals. Increased regulation will help mitigate this to an extent, as is happening already today in some popular cities.
I'd say take the jump, indeed you have nothing really to worry about, at least nothing that couldn't happen booking a hotel or using any other rental site.