Database-as-a-Service

Database as a service providers are rapidly increasing. These are a few I found

SQL Azure
SQL Azure delivers cloud database services which enable you to focus on your application, instead of building, administering and maintaining databases. It is built on SQL Server technologies and is a component of the Windows Azure platform.
http://www.microsoft.com/windowsazure/sqlazure/

VMware vFabric Data Director
The first database supported on Data Director is VMware vFabric Postgres 9.0 (vPostgres),..
http://www.vmware.com/products/datacenter-virtualization/vfabric-data-director/overview.html

Project RedDwarf – Database as a Service
http://www.openstack.org/blog/2011/04/announcing-project-reddwarf-database-as-a-service/

Amazon Relational Database Service (Amazon RDS)
Amazon RDS automatically patches and backs up your database, storing the backups for a user-defined retention period and enabling point-in-time recovery.

You benefit from the flexibility of being able to scale the compute resources or storage capacity associated with your relational database instance via a single API call. Amazon RDS supports both MySQL and Oracle Databases
http://aws.amazon.com/rds/