No. You do not need an Elastic IP address for all your instances. By default, every instance comes with a private IP address and an internet routable public IP address. The private address is associated exclusively with the instance and is only returned to Amazon EC2 when the instance is stopped or terminated. The public address is associated exclusively with the instance until it is stopped, terminated or replaced with an Elastic IP address. These IP addresses should be adequate for many applications where you do not need a long lived internet routable end point. Compute clusters, web crawling, and backend services are all examples of applications that typically do not require Elastic IP addresses.