Did you know that many Cities, Towns and Counties have tree ordinances? Some have view and sunlight ordinances too. All the rules are particular to the location, but they most often call for a permit to cut down trees of a certain size, type or number. If you want to cut down one of the "desirable" trees in your town (say a redwood in Mill Valley or an oak in many places), you usually will need an arborist's report, giving your reasons, such as disease or decay. Use this handy site for finding your town's ordinance.
Sometimes, there will be hearings and your neighbors may speak out. When, as in the last post on this blog, someone wants to cut a heritage oak for construction, where those trees are protected, that might not be a good enough reason. Especially if the neighbors cry foul.
On the other hand, if you have an "undesirable" tree, such as Eucalyptus just about anywhere, acacia or fast growing pines or cypress (note, if you live on the Monterey Peninsula, proceed with caution if you want to cut a native Monterey cypress), your neighbors may cheer. They may even press the Town fathers to make you take down these trees if there is a threat of their falling on their property.
I recently had a case where an almost entirely dead tree of the "undesirable" type loomed over my client's house, making her fear to be in her own backyard. A certified tree risk assessor deemed it a hazard, but it took a judge, and a stern warning about contempt of court, to get the tree down.
This is a costly way to proceed. If your neighbor's tree is a threat to your well-being, make sure the threat is real, talk to your neighbor about it, know what the law says in your Town and consider mediation before bringing in the legal guns.