That said, I don't think most people think using the cloud means that downtime is a thing of the past. I think the more attractive proposition is when hardware breaks, or meteors hit the datacenter, etc, it is their problem, not yours. You still have to deal with software-level operations, but hardware-level operations is effectively outsourced. The question is if you think you can do a better job than Amazon -- some companies think they can, most startups know they can't.
S3 probably fits the description of a cloud service. You send your data, and the service worries about making it redundant without your intervention. If data in NE USA is unavailable, the service will automatically serve you the data from somewhere else. You don't need to know how it works.
EC2 and some of these other building blocks, however, I would not consider to be cloud services. Merely tools for building out your own cloud services to other customers who then shouldn't have to think about failover and other such concerns.
If you know you are using a server that is physically located in a certain geographic location, it need not be represented by a cloud. It is a distinct point on the network.
Cloud hosting is not drastically different from any other type of service and is still vulnerable to the same problems.