Recently I started working with the Amazon EC2 (more) and have been pleasantly surprised. In about 20 minutes I was able to create my own Windows 2008 R2 Data Center Edition Server in the cloud with enough space to run Tableau Server.
Choosing one of the basic configurations from Amazon makes life easy to provision enough horsepower to run a product like Tableau Server but of course there are many more ways you can customize your instance to meet you or your customers needs. Full disclosure, I plan on offering cloud based Tableau Server hosting to my consulting clients so my idea that cloud services like hosted Tableau becoming the new standard for niche BI vendors is a clear alignment of interests.
That said, from start to finish I had a fully functional Tableau Server environment within an hour and was able to access it externally as well. One downside I see here is the lack of Active Directory integration for clients however, Tableau fully supports this, there would just be some networking voodoo needed to make it work.
Without Active Directory integration Tableau Server uses forms based authentication. This means you have to setup each user individually or by script. All in all the trade offs between trying to deploy an on-premise Tableau Server implementation and a cloud based one, the cloud one is definitely attractive.
I haven't fully explored what all the EC2 has to offer however I can assure you that as I start offering it to clients I'll post updates about the ins and outs of using Tableau Server on the Amazon EC2 cloud environment.