Please correct me if I'm wrong, but it seems to me that with this service Amazon is providing the hosting service with network and system administration such that they stand up the instance and manage the administration of it allowing us to focus on the database stuff. Does it have the same physical limitations as SQL Azure? If so, then what's the advantage of their approach?

Several people have questioned the security aspect wondering if Amazon would just help themselves to the code or data in the instance. It seems to me that this could be a potential issue for any hosted system regardless of the level of administration. For example, many organizations pay hosting services to host a server and a NAS but do the bulk of administration themselves. Personally, I would love to have the same level of support without the O/S administration so all I needed to focus on was the database but I'd make certain that the contract protected my intellectual property!