As some of you have already mentioned in the comments, you can use DopBox as a server to sync your KeePass database on your iPhone.
You must use you public folder at the moment, but you can delete your database immediately after your syncing. We are working to support HTTP authorization in the next version.
1. Copy your KeePass database to your public DropBox folder.
2. Display the DropBox URL for this file.
3. In the Server field, type in your DropBox URL without the database file name:
4. Press the “+” button and type in your database file name:
5. Press the “Open” button and type in your database password.
6. Delete the KeePass database file in your public DropBox folder.
Hints: If you are getting a error message “Database is corrupt”, then your username or your password is wrong, or a web authorization is required, which is not supported by iKeePass at the moment.
You can use the settings above to get a test database for iKeePass and check the DropBox way of syncing.