My mother has several brown spots like this and calls them brown warts. Her doctor told her that if she wanted to have them removed he could use laser surgery to get rid of them.
Since they are so common in the elderly, he told her she would probably get more of them, and that they would not turn in to cancer or anything.
Since they are mostly on her back and shoulders, she has decided not to have them removed yet. Her doctor told her there isn't really anything you can do to prevent them.