Update: This solution also removes the annoying sign in request from Picasa that is seen on some android devices.
When you first start using an Android phone it will request you to sign in to a Google account. Doing so automatically triggers a process that syncs your data and photos from your phone to your Google account and vice versa. This synchronization also downloads all your old Picasa web albums to your phone.
While this is a useful feature at times, it tends to be a problem when you really don’t want those pictures on your phone or need to save the space on your phone. Then it makes sense to disable this feature. Here is how to do it: