I've used Relayrides a couple of times, but not for long-term rentals. I loved it. I only picked cars that had multiple good reviews.
The only downside is that because the car owners are people with other jobs and a life, you have to make sure you are very punctual at pickup and dropoff. This isn't as important when you are renting from a car-rental agency. Other than that, if the price is right, and there are lots of good reviews, I would have no hesitation.
Of course, it goes without saying that you should contact your insurance company to make sure you are covered. I was, so it was a no-brainer.