Can I replace my 205/65/15 tires with 215/65/15 tires?
 

Car is a 2004 Honda Accord. Some say they would be too wide and would cause a problem during tight turns.

you may need new rims, and it might rub on the inside of the wheel well

That should be fine. Like the others said, as long as they clear the wheel wells. According to my steering and suspension book, changes of up to ten are allowable on the first of the three numbers

The extra 3/4 inch wider will have no effect on the turning radius or the performance of your car

Yes it will be fine but your tire will be about 1/4" taller and about 3/8" wider. If you start making bigger width (1st number) changes without lowering your aspect ratio (2nd number) your speedo will read low but this is too small to make a difference. The closer you stay to your original total tire diameter the less your speedo will be off.1st number - tread width in mm2nd number - aspect ratio which it used to calculate tire sidewall height in mm (tire sidewall height = tread width x aspect ratio) remember you need to double the sidewall height and add your rim size for a total diameter and make sure you convert all your units.3rd number - rim diameter in inches