I have a Norway Maple that I think is very sick. Some branches are completely dead on one side of the tree and some others still have leaves but they have gone brown. There are also some thin, stringy mushrooms growing on it. I feel foolish since it was OK in the spring and somehow I didn’t notice til now that things had gone wrong! I wonder if it is verticillium wilt
Norway Maples are indeed very susceptible to verticillium wilt. And the “mushrooms” may well indicate that the tree might have been ill for a long time, so that there is dead wood present. Usually in the case of wilt, you notice the leaves yellowing before they fall and often the leaves are smaller than usual from the outset. However, the only way to really tell if it is wilt and which strain it is, would be through testing. Here is a link to a Guelph Diagnostic Lab document, which includes a good picture of what you may expect to see if you scrape the bark back on one on the diseased branches, as well as full details about the disease, a list of plants that are very susceptible and another list of those that are not. It also includes the contact info for the Lab.
One reason to have testing done is to determine which strain is present. In one case, Verticillium dahliae, the fungus can stay in the soil for many years; the other, Verticillium albo-atrum, is usually only present for two years or so. That will inform your decisions about future planting in that part of your garden.
I would strongly suggest you contact a local arborist, who can examine the tree and, if it is indeed, badly diseased, help you go through the process of getting permission to have it removed … and then remove it for you, of course. You can find certified arborists through the Ontario branch of the International Society of Arboriculture website here.