I have owned my 2011 Sonata SE for 12 months/11,500 miles so far. I have not had any problems with it so far except the check engine light that came on, stayed on for a couple days, then went out on it's own. Since 90% of the time the check engine light is either the gas cap or some other emissions item, I ignored it since the car ran fine. The Sonata has had several minor recalls in the last year - door latch (1200 cars), steering column bolts (all cars, but just a checkup), a couple ECU reprograms. While I have had no problems with mine, I have seen others with noisy fuel pumps - a constant hum from the gas tank, a couple bad tranny's, and alignment concerns are common. Hyundai's in general are prone to alignment issues. I sell them, and it is a common complaint for a customer to say their car pulls to the left/right. It's not just the Sonata.
My beefs with the car are the suspension tuning - it's just not the right balance of sport/comfort (I have the 18" wheels), interior squeaks, and the paint, which is easily damaged. Overall, though, it is an impressive combination of style, performance, room, features, and price. I am not disappointed in mine, and am glad I sell them for a living.