Amazon's recent outage has brought up many questions about the "safety" of cloud computing. The problem (beside Amazon's lengthy outage) is mainly that there is a lot of magical thinking about cloud computing. It is not a conjuring trick that allows the user's organization to depend on the cloud vendor for everything, but rather a computing platform that requires thoughtful architecture, implementation, and management.
Not every public cloud is the same -- some offer mainly raw compute power (and perhaps storage and tools) -- others offer a managed computing experience. Users need to know what they are buying and plan accordingly. As Jonathan Spira points out in his article on the Amazon outage, companies who planned for trouble (and spread their data and computing over multiple sites) did not have a problem.
Cloud Compouting is a great way to avoid the cost of implementing and managing infrastructure; what you run on that infrastructure and how successful the results will be depends on the skill and effort your team put into the work.