I work with a number of high traffic sites (TB's of data each day, 10's millions page views/month). With many of these sites, we have offloaded static content to either dedicated static content servers (typically cloud based so we can scale up and down) or to content deliver networks. I've not had anyone report any SEO impact.
In contrast, they often see user engagement (page views/user), repeat visitors, and other traffic metrics improve. Users like fast sites. Also, Google apparently likes fast sites too, so while I've not seen it, you could actually get a boost in your SERPs due to faster loading pages.
If you break down a modern web page, you will find numerous elements required. Dozens of images, CSS, javascript as well as the page itself. All of these items require a request to the web server.
With some graphic intensive sites, I've seen as much as 95% of all web server requests (HTTP requests) be attributable to static content. By moving these HTTP requests to other systems, you free your primary server to handle the application. This provides a better user experience and improves scalability.
Content Delivery Networks
I do not use Amazon's Web Services so I do not know specifically what they offer. But here are two CDN's Ihave used with good success:
Internap:
http://www.internap.com/cdn-services-content-delivery-network/
Edgecast:
One method I look for is called "origin pull." With this method, you do not have to upload files to the CDN. The CDN will fetch them automatically from your site as needed. I found this is much easier to manage on sites that have frequent content updates.
