I'm still shocked to read that people assume that Content Delivery Networks are expensive, most charge as little as 0.20c per a GB.
Serving static websites on CDNs is amazing - you get the performance of a dedicated server without actually paying for it, plus you have a server in all major regions around the world so effective its actually better than a dedicated server for speed and scalability.
There are a few major setbacks when hosting on CDNs, and these are:
No PHP files
Sadly most CDNs don't support non-www CNAMEs so you can't resolve the domain when someone forgets the www, not a major problem but there are ways around this. You setup a EC2 or shared hosting and you let it handle the non-www with a redirect. So whenever someone forgets the www it communicates with the server, then redirects to the CDN correctly. An alternative method is that you pick a CDN which supports this - I believe Limelight does, but Amazon and Rackspace do not. I've heard Limelight hosting the DNS and making edits manually on their system, I've never done this myself so I can't confirm they do or do not.
The other set back is that you need to purge the content or files that your editing, so say for example you make some additions to the index.html you'd need to either setup a short expire on the container or manually purge that file from the cache so it updates all over the world.
Hosting a static site on a CDN is fanstatic - I run a handful of static sites on CDN and they are fanstatic, I only use like 1-2GB on each site and I get bills for £0.24p for each site, which is cheaper than shared hosting, and gives you the performance of a dedicated server. If your going to setup a small VPS other than a EC2 for the redirect any VPS that is 128mb will do it. You can get a cheap one for like $1 a month. Just Google 128mb VPS or VPS under $5 a month - there's hundreds of companies doing low spec VPS for peanuts which will do the trick.