I have 185 65 15 tires on my Honda. I want to go up at least a size but some tire people say it will rub. Will 195 or 205 60 or 65's on 15 inch rims rub the body?

 

It depends entirely on what has been done to the car. If you're running it pretty low, you may run in to issues with clearance. But, at stock height, there will be little to no difference between 185/65/15's and 195/65/15's. 205/60/15's could require some work.