Ideally, you want to build cities just beyond your existing city's "Fat Cross" (refer to pg. 62 of the Game Manual [I have the Pre-Order Edition though, so the page number might be different for the regular edition's manual]), which is the city's maximum radius.
If two cities radii overlap, it decreases both of their maximum growth, production, and commerce -- so it's rarely worthwhile. There are a few exceptions, which I won't go into, but you should generally avoid overlapping city radii.
However, you don't want to build too many cities either, because of the new Maintenance system that penalizes you according to how many cities you have. Consult page. 177 of the manual for an explanation of "ICS" (a.k.a., "Infinite City Spawl"), which explains why it isn't a good idea to build too many cities too close together.