I found an article from 2008 discussing how to call Java code from MySQL. There were a lot of caveats and disclaimers because the process involved working with an experimental branch of MySQL.
For a project I have in mind, it would be very useful to be be able to access Java libraries within MySQL, analogous to Oracle's Java Stored Procedures. Does this capability now exist as a standard feature of MySQL? If not, what open source RDBMSs support something similar to Oracle's Java Stored Procedures?
PostgreSQL supports pluggable procedure languages, and a project exists to extend PostgreSQL with PL/Java as the language.
I don't recommend putting too much code in the RDBMS. Tools to develop, test, and debug code in the application layer are better than tools for code in the RDBMS.
Also many developers don't understand that code inside the RDBMS should obey transaction isolation. They try to send emails from triggers and so forth. I think code with side effects should be in the application layer, so you don't create phantom effects (e.g. an email may notify of a database change, even though the change was rolled back).