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You can trim back branches to your property line, but that may not solve the problem if you're worried about the whole tree coming down.
City governments often step in to take care of, or make the owner take care of, dangerous trees. Some cities have ordinances that prohibit maintaining any dangerous condition -- including a hazardous tree -- on private property. To enforce such an ordinance, the city can demand that the owner remove the tree or pay a fine. Some cities will even remove such a tree for the owner. See How to Find Local Ordinances and State Laws to locate your city's laws and policies on trees.
You might also get help from a utility company, if the tree threatens its equipment. For example, a phone company will trim a tree that hangs menacingly over its lines.
If you don't get help from these sources, and the neighbor refuses to take action, you can sue. The legal theory is that the dangerous tree is a "nuisance" because it is unreasonable for the owner to keep it and it interferes with your use and enjoyment of your property. You can ask the court to order the owner to prune or remove the tree. You'll probably have to sue in regular court (not small claims court) and have proof that the tree really does pose a danger to you.