Seeking spam filter that uses a database shared by all its users
The short answer to this is NO.

I think you are confusing Gmail's SPAM filtering methodology with single user methodology.  What you have to remember is that Gmail is a cloud based service and it IS providing mail service to billions of users.  So, even though you have a single email address with SPAM filtering, it's filtering for all users.

Additionally, SPAM filtering is a "learning" process - meaning the system learns what SPAM is as it goes.  The moment you take it from the cloud (or server) to your local machine, it can't learn from other email accounts.  (Which is why you want to share the database)

Once you have to create an infrastructure to start sharing the database to be able share what it has learned, you would have found it's easier and cheaper to set up a mail server and use a SPAM filter module. 

My suggestion is to use a cloud based email provider.  I personally use hosted Exchange directly from Microsoft and I pay on $48 per year for this service.  In addition, I have a "private" email address I only give to colleagues and "disposable" email address I use when registering for websites, trade shows, and product downloads.  Using this technique I can easily identify SPAM; the result is that I have an extremely clean mailbox.