New Jersey residents can trim a neighbor's trees, but only if the trees are growing over their property and only as far back as the property line. For example, if a tree's branches come over a neighbor's fence into your yard, you can trim its branches back to the fence line.
While you can trim the tree, you still have to live with the neighbor. For courtesy's sake, talk to your neighbor before you cut back the tree, and give her the chance to prune it. If she doesn't do it, trim your side of the tree.
The law that empowers New Jersey residents to trim neighbor's trees dates from 1927. This law covers tree branches, but it does not cover tree roots that grow onto your property.