It's very hard to determine real figures, and few exist for the 'free' databases.
MySql is favoured with hosting companies running *nix.
Whilst Access is favoured for the cheaper hosting on Windows (SqlServer for the most expensive hosting).
Oracle, DB2, Informix and Sysbase are all more used for Enterprise level sites and for non-Internet work (such as the customer database at British Telecom which isn't web-facing).
As an indication you could cite Netcraft's web server listings...
http://news.netcraft.com/
These show the following splits of web servers:
Apache 63.72%
Microsoft (IIS) 25.95%
Zeus 1.81%
SunONE 1.59%
You can guess that Zeus and SunONE are run by larger corporations with support needs. Plus they only account for a small part of the whole.
With IIS it's undoubtedly going to be MS Access or SqlServer (though it is possible to install MySql or PostGres onto a Windows machine and for it to cope well).
With Apache it's most likely to be MySql (though again it's possible to ODBC through to another database)*.
This rather primitive deduction does support that the most prevalent database would be one that runs on *nix and integrates well with Apache. As Linux comes with Apache, PHP and MySql it's pretty obvious where to place your bets.
So I would guesstimate that MySql currently outnumbers the total of Microsoft databases on the web 2 to 1.
However... it should be noted that I'm not a MySql fan... I'm an Oracle fan... but it should be further noted that the site you're on runs on MySql
*
http://news.netcraft.com/archives/20...truggling.html shows that no more than 7% of Apache installations are on windows which reduces the likelihood of Apache being run directly against MS Access or Sql Server.