I believe Godaddy's Virtual Server Space is a VPS service, not a cloud computing platform. I also don't think Amazon offers such a thing as "Simple Web Services". They do offer Amazon Web Services, which is a whole host of cloud services, including Amazon S3 (Simple Storage Service) and Amazon SQS (Simple Queue Service) and Amazon SNS (Simple Notification Service), but you're probably looking for Amazon EC2 (Elastic Compute Cloud). And Google App Engine is another popular cloud service, which is far more widely used than Godaddy's Virtual Server Space.
The differences are mainly going to be pricing, architecture, and how the service is managed and integrated. Google App Engine is Java- and Python-based. So if you use PHP, then you won't be able to use App Engine. Azure is Windows-based, however it uses FastCGI so it can use almost any programming language. Amazon EC2 is much more like a VPS service in that you're managing individual virtualized servers. So you can pick what OS and software to load onto it. Also, because of this, EC2 applications will be much more portable than applications that have been designed specifically for App Engine or Azure.
Additionally, each cloud platform has their own unique feature set. AWS offers a few cloud storage options separate from EC2. Google App Engine comes with DataStore, which is based on BigTable, and Azure comes with its own set of storage services. Naturally, AWS services are easier to integrate with one another. Likewise, App Engine (for Business) can be closely integrated with Google Apps.
Lastly, you should know that pretty much all web hosts allow you to manage multiple sites on a single account. DreamHost, for instance, lets you manage an unlimited number of domains and subdomains on even their most basic hosting plan. So that's not a unique feature of Godaddy. You don't need to "think about" hosting with any decent web host. Though with better web hosts you do have a lot more control and freedom over customization than you get with Godaddy.