When buying from a dealer, you may receive a limited warranty (perhaps 30 days) and many dealerships offer manufacturers' Certified Pre-Owned programs for their late model cars that can extend the warranties out a number of years. Some advantages of buying from a private party include a lower price, you will have all the repair records (if they are available) and you know the previous owner, should any questions come up later.
Most private party cars are not in perfect condition, which is why Kelley Blue Book's Private Party Values are usually much lower than used Retail Values. Most of the time, the seller and buyer assume the car is "AS IS," but there are always exceptions. Also, most sellers add in a few hundred dollars to the asking price for negotiating. Unless the seller specifically states the intention of a "firm" price, there should be room for some negotiation.