Bukkit

To use MySQL, you will need to use an external jar file.
Using external jar files with jython is a bit tricky because it has to modify the classpath at runtime. We're using a trick called "ClassPathHack".

Download MySQL connector

1. Create a new directory (in your server's dir) called 'lib'
2. Download mysql-connector (platform independent)
3. Open the archive and extract 'mysql-connector-java-X.X.XX-bin.jar, save it as 'mysql-connector.jar' inside the 'lib' dir

Create ClassPathHack

Copy the script below and save it as 'mysqlhack.py' in your plugin's directory

import java.lang.reflect.Method
import java.io.File
import java.net.URL
import java.net.URLClassLoader
import jarray
from java.lang import Class

jarfile = "lib/mysql-connector.jar"
driver  = "com.mysql.jdbc.Driver"

url       = java.io.File(jarfile).toURL()
sysloader = java.lang.ClassLoader.getSystemClassLoader()
sysclass  = java.net.URLClassLoader
method    = sysclass.getDeclaredMethod("addURL", [java.net.URL])

method.setAccessible(1)
jarray.array([url], java.lang.Object)
method.invoke(sysloader, [url])
Class.forName(driver)

Connecting to MySQL

Make sure you have zxJDBC installed, then use something like this:

import mysqlhack
from com.ziclix.python.sql import zxJDBC

mysql_database = "jdbc:mysql://localhost/db_name"
mysql_user     = "john_doe"
mysql_pass     = "secret"

conn = zxJDBC.connect(mysql_database, mysql_user, mysql_pass, "com.mysql.jdbc.Driver")
curs = conn.cursor()
curs.execute("SELECT * FROM users WHERE name = ?", "Jane Doe")
results = curs.fetchall()

The jython website has more info on zxJDBC.