No. You also cannot cut your neighbor's grass or bury his dead grandmother. But seriously, no, of course you can't. To do so would require a trespass onto his property, which would itself be illegal.
cut down
Take photographs and make certain you mark your boundary clearly in those photos. Get an estimate for a replacement (tree + delivery + planting) and ask the neighbor to reimburse you. If they refuse you could file suit in small claims court.
The tree trimmer or his insurance company.
Get an attorney to advise you.
A neighbor cannot make you cut a tree down. BUT if your tree encroaches on a neighbor's property, causes a risk to a neighbor or their property, or causes a situation that prevents a neighbor from full enjoyment of their property, the neighbor can ask a court to make you cut back the limbs that are causing problems for their property. Your rights end where the property line begins; same for your neighbor.
um u need to talk to your neighbor and ask if he or she can allow you to cut it down
The carpenters son.
If a human cuts down a tree that was giving shade the sun can erode rocks below the tree.
a lumberjack... leaping from tree to tree in the mighty rivers of british Colombia
If your neighbor refuses to cut down the tree, use insurance or savings to cover taking down your fence (and putting up a new one), get him/her to sign a paper that says he will hand his tree over to you in exchange for a portion of money from, then put up the fence (or wall, in this case), and do with what you will to the tree. If that doesn't work, move, or trespass property by cutting down the tree, and risk getting sued.
If the tree belongs to your neighbor, it is their responsibility to maintain it. Try talking to your neighbor about the situation and see if you can resolve it together.
a lumberjack... leaping from tree to tree in the mighty rivers of british colombia
Usually, people who ask this question really want the answer to a different question -- can I trim a tree that encroaches into my land, can my neighbor cut down a tree that is on our mutual property line, can I take down a tree on my neighbor's land that poses a risk to my house? I point this out not to sound like a jerk, but only because the legal answer to "who owns the tree" doesn't usually answer the (real, underlying) question. Where a person plants a tree on his/her property that grows into a neighbor's property, the tree still "belongs to" the person who planted it. When nobody knows who planted a tree, the tree usually (that is, in most states) "belongs to" the neighbor on whose property most of the tree is now located. However, whenever a tree crosses property lines, whether it is the roots or the branches or the trunk that cross the line, the person on each side of the line can pretty much do whatever he/she wants to the tree on his/her side. Think of your property line as a geometric plane that extends up into the sky and down into the ground. If you don't like the branches on your side of the plane, you can cut them, no matter who "owns" the tree. If you don't like the roots on your side of the plane, you can grind them up. As a practical matter, this rule means that whenever one neighbor wants a boundary tree taken down, it will be coming down, because even if the tree-loving neighbor does not agree to have the work done (which is important - it means that most arborists will not agree to do the work), the tree-hating neighbor can still do enough violence to the tree on his/her side of the line that the tree will soon die and need to be removed. If you're in Massachusetts and have a boundary or other real estate question, call the Law Office of David R. Baron in Boston.