I spoke with a friend of a friend yesterday about his house. His neighbor is doing a teardown and building what appears to be a McMansion, with the foundation being oh so close to the property line. The prospective client was smart enough to call BEFORE anything happened to ask about possible remedies and solutions.
One is zoning. Does the zoning permit a side yard so narrow that you can build almost or right to the property line? If not, then you have a bone of contention with the neighbor when it comes time for a variance or a rezoning.
Another possibility: lateral support. In Illinois (and I'll bet most states), the landowner has a duty not to change his land such that it materially and adversely changes natural support. If the new building starts causing problems with the neighbor's foundation, for instance...you see where I'm going.
There's other things to think about too, but I like to think about horses before zebras.