I've noticed that this question has come up periodically on this listserv.
I've always hoped that someday someone might find a recording that can be
verified.  Last year, I ran across a reference in this source to something
that gave me a little hope:

Rust, Brian A. L.  Discography of historical records on cylinders and
78s.  Westport, Conn. : Greenwood Press, 1979.

There is a citation to a speech that Twain supposedly recorded; Brian Rust
puts the date at "1895?", as I recall; it's been a while since I saw the
reference, and my memory might be inaccurate.  The citation, however,
does not say anything about where this recording is kept.  If Mr. Rust is
still alive (he'd be 75 now), he might be able to provide more details.
This is an intriguing work for anyone interested in historical recordings;
I was intrigued to learn, for example, that there are recordings of people
such as William Gladstone.

Best regards, Jim Edstrom
 On Mon, 11 Aug 1997, Lymans
wrote:

> Greetings,
>
> I've seen at least one moving picture of Mark Twain, but
> I've never heard his recorded voice. I've wondered about that.
> Certainly Mark lived well into the age of sound recordings.
> It seems inconceivable that no one would've thought to commit
> his voice to wax, the famous man that he was -- unless of course
> Mark refused. Is there such a recording of his voice in existence?
>
> Paul Lyman
>