A credible estimate of the number of people actively using Microsoft
Access to develop database applications. (Note: this is not the same
as how many people *use* Access, or have it installed on their
desktop. And it is not just "professional" developers.) I would also
like some breakdown into categories such as corporate/small
business/professional developer/etc.

Just a gut feeling, but I would think anyone still using this as a
"serious development tool" for a real package, which they hope to
sell, would be in the small business area. It can be used (with an
ODBC connection for instance) to attach to a real database, and this
could be feasible for a "larger small business", but really, there are
better tools out there, and all of them are much cheaper to develop on
(MySQL for example is probably the best database out there and it is
free to use, develop with, and install).

MS Access is great for "clay" programming. It is fast enough in the
development area to get some ideas down, and see how they really work,
but when it is time to start selling, ... it still isn't marble. Many
developers have found that the backlash of support from their clients
support needs, far out weights any savings gathered in from saved time
in development.

But again, these are just my gut feelings on your question. 

webadept-ga

Yeah, Access is only going to be used for very small business
applications. Probably for businesses that only have one computer
acutally. There are some advantages to using it for an application
that will only run on one machine however. First when you build a
database in access you can use the integrated Visual Basic tools to
create a nice frontend for it, you can simply save the database you
are working on and give it to someone else who can then open it in
Access and use the frontend that you wrote in conjunction with the
database with no setup. Second, the engine can be exported to an
executable file containing Visual Basic code (i think this is only if
you use the full Visual Basic development suite) so that your small
application can have a database included. Makes for easy distribution.

I would guess that there are a lot of small local application
developers building very basic database applications for clients and
friends in their local markets. That still doesn't make it a "serious
development tool", more like a home do it yourself kit for
straightforward projects.

I have seen very old version of MS Access applications that were being
shared on a network of 12 computers running windows 95.
Microsoft claims that new MS Access can handle 256 simultanius
connections. I don't think that's a true statement and a more
realastic number should be around 100 simultanious connection.
The speed of the transaction is very much dependent to how fast your machine is. 
Access is a very fine RDBMS and has load of features that many
professional databases still don't have such as views or more recently
i belive stored procedures.
Also be aware that Access can not handle large tables with a lot of fields and keys