What Rasidel says may be true. I dont autocross my car, i dont take corners fast, i dont really care too much about handling.
My car goes in a straight line, and gets me to and from work.
I enjoyed every minute of driving my car with those wheels and tires... I never felt that the cars performance was significantly hurt in that department, and when i bought the car, it had much smaller wheels in back.
I have 315's on 11" wheels now, and the same exact tires up front, and still have no problems. Granted, the front WHEELS are wider now, but not the tires.
Regardless, the question was asked "what is the biggest" -- and 315's are about the biggest you can get.
Some people like it, some people dont. I personally, loved it.