Used cars have come a long way. Back when cars seemed to wear out after 5-6 years, buying a used car was a risky proposition. Today, with all the advances in technology, cars last longer and are more reliable than ever. In 2012, the median age of a car in the US was 11 years old and had over 100,000 miles.
It used to be that a used car was a car a new car dealer took in on trade and moved to the back of the lot, so a guy in a plaid suit could have a job. Today, used cars are big business and are more profitable to sell than new cars. Part of this reason is that more new cars than ever are leased for 2-3 years and then turned in to the manufacturer. The manufacturer then runs the leased cars through an auto auction, where they are bought and transported to your local dealer.
The biggest advantage to buying a used car is price. New cars depreciate 30-50% in value over the first three years of their life. By buying a 2-3 year old car, you take advantage of the depreciation instead of taking the hit. It's a good way to buy a car that sold for $40,000 new in 2011, for $25,000 today.
The drawbacks of a used car are primarily age and mileage. You're getting a car that is several years old and may no longer be covered by the new car warranty. But there is an exception to this rule on "Certified Used" cars, which offer some of the benefits of a new car, including a warranty, as well as special incentives or financing. What you get for the certified status, depends on the manufacturer, but in most cases it will include a one year warranty and the same financing rates or terms as a new car.