Can I trim my neighbor's trees that are growing onto my side?

My neighbor refuses to get a tree person to come out to trim his trees and he has threatened me if I do it myself. There are horrible cherry branches that make a huge mess on my lawn every year and attract all types of terrible birds. What sort of laws...

are on my side for cutting down the errant branches?

well there are no laws stating that you can cut them your self so go and stand up to that man and tell him "im sick of asking you nicely to get those trees off my lawn im going to do it my self "
and if he threants you or tries to hurt you then you call the police or you buss him dead in the face that is if he tries to hart you then you can say you were defending yourself lol

I have my realestate license in Tennessee. The answer is yes, as long as you trim the tree branches that is over your property. Every property owner has what is called "Air Rights". "Air Rights" is the right that a property owner has to control the air space above his property.

Real Estate Glossary (see definition for "Air Rights"
http://www.brownharrisstevens.com/guide5.aspx
http://www.prou.net/utilities/glossary/glossary01.html