Azure: Replication Beginner help
Traditionally SQL Server relied on technologies like SQL Server Replication, Log Shipping or Change Data Capture/Change Tracking to replicate data across multiple locations. Unfortunately none are available in SQL Azure. Instead SQL Azure has the SQL Data Sync feature:


  SQL Data Sync (Preview) is a service of SQL Database that enables you to synchronize the data you select across multiple SQL Server and SQL Database instances. To synchronize your data you create sync groups which define the databases, tables and columns to synchronize as well as the synchronization schedule. Each sync group must have at least one SQL Database instance which serves as the sync group hub in a hub-and-spoke topology.


At this time SQL Data Sync is in preview and has some known limitations. 

Also SQL Azure does offer backup/restore and export/import features, see Windows Azure SQL Database Backup and Restore, but these are all 'copy everything' solutions, not 'copy only what is changed'. 

A possible solution is to switch to SQL Server on Windows Azure, which gives you a traditional SQL Server instance capable of doing all the technologies above, and you can have it replicate data to a SQL Server hosted on Amazon EC2. See Provisioning a SQL Server Virtual Machine on Windows Azure.