We've had very positive experiences renting. We just booked our fourth DVC rental with David's Vacation rentals. (Past ones: a week at the Villas at Wilderness Lodge in a 2-bedroom villa, 3 nights in a Beach Club studio, and 2 nights in a Polynesian villa: upcoming, 3 nights in a Grand Floridian resort studio villa). On one occasion, we also rented through a MouseOwners member who was thoroughly-vetted and had excellent references and a solid written contract (although changes to that board have made such rentals a little more difficult to arrange), for a one-week stay at a studio at Animal Kingdom Lodge, Jambo House. We've also put in requests with the DVC Rental Store, and although they didn't have a member with the points we needed, we were favorably impressed with their customer service and wouldn't hesitate to use them in the future.
DVC rentals have literally made stays at deluxe resorts a financial possibility for my family, by giving us rates anywhere from 35%-50% less than rack rate. I'm a big fan!
As others mentioned, one downside is that you can't usually modify or cancel once the reservation is made (at least, not if you reserve through the reputable go-between companies: when we privately contracted with an owner, she did have a provision in her contract that allowed for a one-time rescheduling in the event someone got sick or our travel plans were interrupted). This also means that if Disney releases a special offer for your dates (e.g., dining promotion, room discount), you will not be able to take advantage of it. If you're afraid you might have to cancel your plans for any reason, you'll either have to accept the risk, or find a travel insurance that will cover you if needed. Another way to potentially insulate yourself from travel delays or short-term illness is to structure your trip as a split stay, with the first half being an arrangement you can cancel on short notice without penalty, and the second half being a DVC rental.