This week's book giveaway is in the OCPJP forum. We're giving away four copies of OCA/OCP Java SE 7 Programmer I & II Study Guide and have Kathy Sierra & Bert Bates on-line! See this thread for details.
I suggest you to use Awake SQL, a virtual JDBC Driver that is supported on Android with a dedicated packaging. Awake SQL is Open Source (LGPL v2.1).
Disclaimer: I'm the author of Awake SQL.
Awake SQL allows you to code JDBC calls in Android. The JDBC calls are routed through HTTP and executed on the remote server. The result is sent back using JSON.
The database is not accessed directly: the JDBC calls are filtered by a (configurable) Servlet on the remote server.
Awake SQL supports all major Open Source and commercial databases.