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.

Memcache on AWS

ElastiCache is protocol-compliant with Memcached. Therefore, you can use standard Memcached operations likeget, set, incr and decr in exactly the same way as you would in your existing Memcached deployments.   Existing applications do not need to change and can simple 'pointed at' the ElastiCache service.  ElastiCache is exposed at the same port (11211) as default memcache port.  To configure and manage the cache servers for your application, you will need to use the AWS Management Console, CLI, SDK, or web services.