Living in the United States it is sometimes easy to forget that some companies are much more America focused than others. Microsoft will offer some of it's betas to the North American region only, but products are usually available worldwide. Windows Azure, as a beta, is offered worldwide.
Amazon EC2 (RTM) has been offered in North America only, but has made the jump across the pond to Europe. In my mailbox today:
"We are excited to announce that we have extended Amazon Elastic Compute Cloud (Amazon EC2) to Europe. Developers and businesses can now run their Amazon EC2 instances in the EU to help achieve lower latency, operate closer to other resources like Amazon S3 in the EU, and meet EU data storage requirements when applicable. The new European Region for Amazon EC2 contains two Availability Zones enabling you to easily and cost effectively run fault-tolerant applications with the same scalability, reliability and cost efficiency achieved with Amazon EC2 in the U.S."
Amazon EC2 is the Amazon offering for hosting virtual machines in the Amazon Cloud. Windows Azure is a slightly different, but competing solution from Microsoft.
Note: Interested in Amazon services? Some time ago I wrote Introduction to AWS for C# developers.