In some cars it is the brakes for sure. I have a 2008 G37S and you can't get rims to clear the brake that are less than 19" (well, there are a few 18" rims but are generally not widely available). The BMW 335i with sport package also has a hard time with rims less than 18" (which, again, are possible but hard to find that will clear the brakes).
Having said that, I believe esthetics are, for most cars, the reason but I will say that a car with nice 18" rims is FAR more visually appealing than one with 15" rims. Take any car that has, say for example, a base version with 15" or 16" rims and compare it to the same car with an optional "sport" package with 17" or 18" rims and the car with the bigger rim almost always looks much better. Now, once you go above 18" or so, I think it is getting a little silly.