Amazon now provides on-demand “cloud computing” services called Amazon Web Services.
Elastic Compute Cloud (EC2) is a service that let you run linux virtual machines (called ”instances”). You can configure and use the instances for whatever needs you may have.
Simple Storage Service (S3) is the storage solution. It stores simple files (called ”buckets”) and the virtual machine images.
One important note is that EC2/S3 lacks database support. Sure you can use S3 to backup the database but that’s just a hack and I wouldn’t recommend it for production use.
I think that using EC2/S3 is not going to replace a real server for a web services. Nevertheless, I think it can help with scalability issues. For instance, you could use it for a web server or a reverse proxy to answer traffic spikes (see http://hostingfu.com/article/setting-up-part-time-web-cluster-with-amazons-ec2).