AWS : Storing Session State

AWS SimpleDB, Memcache and DynamoDB can all be used.  DynamoDB is a good option as there is already a session provider for DynamoDB :

http://aws.typepad.com/aws/2012/09/managing-aspnet-session-state-with-dynamodb.html

For SQL Server, you can also look at session management in SQL server for persistence  and use built in .net session provider modules.

You can also manage session state using AWS RDS for SQL Server, MySQL or Oracle.