Not too long ago my mother-in-law purchased a 2009 Honda Civic. Her version came originally equipped with the Bridgestone Turanza H EL400-02. Unfortunately this tire suffers from poor tread life and poor all-season traction. After 30,000 miles they are due for replacement.
Naturally she came to me for a few suggestions. Her model has a 205/55-16 size as Original Equipment. As I've mentioned befpre, one of my favorite tires is the Michelin Primacy MXV4. It offers a very smooth ride, much improved traction and tread wear and is great on a Civic.
Another good tire for this car is the General AltiMAX HP. It offers exceptional value, reliable traction and improved tread life.