Playing devil's advocate here (as the owner of a 'nuisence' tree).
We have a beautiful mature ash tree in our garden which we've had professionally trimmed/thinned and generally maintained and it looked lovely although the keys are a real pain when they start falling but that's a small price to pay.
The large house next to us was sold recently and the new owner has done it up and turned it into holiday lets. Without any discussion she announced (via a note throught the door) that she was going to cut the branches from our ash tree that hung over the fence as they were a nuisence to her guest as "branches" (read twigs) were falling on their cars. She's got plenty of parking space so why her guests couldn't park 10 feet to the left is beyond me.
When we approached her she wasn't prepared to negotiate or even discuss the matter and simply became abusive.
Seeing someone up a ladder hacking, there is no other word for it, at our beautiful tree had me in tears. I know she has a legal right to remove the branches that over hang her property but if she'd approached it in a different manner maybe it could have been done by agreement, by a tree surgeon who at least knew what he was doing and to everyone's satisfaction. As it is, the tree looks a mess, our privacy has been invaded and we now have a neighbour we don't get on with (she's subsequently started building a bungalow in another part of her garden and has already broken two of the planning conditions put on the consent - and all this in the grounds of a Grade II listed building and in a small village).
My advice to anyone thinking of trimming a neighbour's tree is to try and talk to them before getting out the chainsaw. Remember that even though the branches may be on your side they may be visable from your neighbour's side and changing his view. Making adjustments that are acceptable to both parties is a much better solution than alienating your neighbour - you never know when you might need them!