I just moved into a new neighborhood and innocently parked my car on the public street. Before I knew it, my neighbor pulled up behind me and started screaming that I'm in "her" parking spot and demanded that I move my car. Is the parking spot legally hers?
Probably not. Generally speaking, an individual citizen has no "ownership" rights to a parking space on a public street. These spaces are open to the public on a first-come, first-served basis, even if people come to believe that a spot in front of their house is theirs.
There are exceptions, of course, in neighborhoods that specifically allocate a particular parking space to the owner or occupant of a particular home. This is most likely to be true in condominium, townhome, or other developments governed by a homeowners' association (HOA). The parking spot would be included in the rental or homeowner agreement. This is rarely the case in large cities like New York or Chicago, but it is more common in suburbs. If you received a set of CC&Rs along with your purchase or rental agreements, read them over to see how parking spots are dealt with.
Given that this person is your neighbor, you would theoretically know whether you also have an allocated parking spot. Chances are, if you don't have one, she doesn't either.
So what do you do about this situation? You could either continue to park in the parking spot and worry about provoking further arguments, or you could engage your neighbor in a discussion. Perhaps the two of you could compromise by determining which of you most needs the spot and when.
For example, maybe you need to park there on weekends and she needs to park there on weekdays depending on your respective work schedules. Perhaps you could trade off, and you could park there one week and she parks there the next. (This assumes, of course, that parking in your area isn't so tight that the spot is frequently filled by someone else entirely!)
Try to make your neighbor understand that you have every bit as much right to park on a public street as she does; it is to your mutual advantage to keep each other's needs in mind so that you can both park in peace.