I didn't know you could do that on Amazon. I didn't think they would allow you to run your own applications.
Do you have any details?
Amazon EC2 essentially lets you build and run a Windows 2008 virtual server within their 'cloud' environment. More information at:
http://aws.amazon.com/ec2/It is a proper, Windows 2008 image, so you can RDP to it and install any Windows application you like onto that image, and run them as if it was on your own server on your network. This includes any Clarion application, MySQL database or MS-SQL etc.
Images come in different sizes, and you can create many of them - just pay by the hour for however long you need them to run.
We have several production images for client hosted NetTalk sites, plus a few test images that we run up and take down depending on our development needs.
You can allocate fixed IP addresses to those images (via Elastic-IP) so that they can be accessed by anyone, and you can give them a proper DNS name such as myapp.mysite.com. No one can tell it is not a 'real' server.
Amazon now also give you a nice management console to manage all your instances and ensure they are still working. For advanced use, you can also integrate your instance with Amazon's S3 Storage services for nearly unlimited disk space...just pay by the Gb used per month.