Just to add to what Steve has said, in most parts of the country the neighbor is at fault when he does things that cause water runoff to "change its natural flow" and go onto your property. I don't know if you want to get into a legal battle with your neighbor, but you should at least find out what the rules/laws are in your area so that you know your rights.
Where does the water flow from his gutter drainpipes? Hopefully not toward your property...
Also, take lots of pictures in case you need them later.