Amazon Web Services is a service that approaches almost every aspect of cloud computing. They offer services such as computing, database, storage, networking, application hosting, web applications, high performance computing, backup, storage, and many more. From my knowledge you are also able to use their services for gaming servers.
Now the true beauty of about Amazon Web Services is that it is fast cheap and extremely robust with tools and applications to get you started quick and efficiently. If you are an individual or business who is dying to get into the cloud world I would seriously recommend checking out Amazon Web Services.