The new Dropbox Android app plays nicely with KeePassDroid. I use Dropbox to synchronize my keepass database, because it is available on all of the platforms I use daily: Linux, Windows, and Android.
It's very easy to use. I install it on my desktop first, and move my keepass database into my dropbox. Then, fire up the Dropbox Android app, and log in:
Navigate to your database and click on it:
In the background the Dropbox app will be waiting to see if you make changes to the database. If you do, it will upload your changes back to your Dropbox.