If and when you do decide to put a set of 18x7.5" wheels on your civic, there are certain things that must be met in order for you to use these size wheels without much problems.

You want to get 18x7.5" wheels with at least a +42mm offset (more would be better, up to a +45mm offset). The tire size that you must mate with these wheels are 215/35/18. Make sure that your alignment is up to specs. If you have a camber kit and a set of adjustable coilovers, that's an added plus.

If you've met all of these requirements, then you could install a set of 18's on your car without much problems. The one other thing that you might have to do is eliminate your inner fenderwell lining. But you rubbing your tires on these would solely depend on how low you decide to drop your car.

A lot of people go for 15's and at most 16's on older model civics, but I think that the newer model civics (usually 7th gen on up) can handle 17's or even 18's with no problems. Of course with these newer model civics, they have bigger fenderwells then their older counterparts, so they can handle the bigger wheels sizes as well as provide room for bigger sidewalls for these wheels.