Eric pretty much nailed it. We (Bitnami) are a popular provider of free AMIs for popular applications and development frameworks (PHP, Joomla, Drupal, you get the idea). I can tell you that EBS-backed AMIs are significantly more popular than S3-backed. In general I think s3-backed instances are used for distributed, time-limited jobs (for example, large scale processing of data) where if one machine fails, another one is simply spinned up. EBS-backed AMIS tend to be used for 'traditional' server tasks, such as web or database servers that keep state locally and thus require the data to be available in the case of crashing.
One aspect I did not see mentioned is the fact that you can take snapshots of an EBS-backed instance while running, effectively allowing you to have very cost-effective backups of your infrastructure (the snapshots are block-based and incremental)