Not all of them do, of course. But many will keep copies of them for at least some period of time. In my state, for example, lawyers must keep the files for work they did for a client for 7 years. Thus, an attorney in my state should keep a copy of the will he did for a client for at least that period of time.
Note, though, that in most states, a COPY of will does not do you much good. A copy can’t be probated—the original must be produced for that. There may be limited circumstances where the copy may be useful, but if you are looking for a will to probate, you probably need to find the original.