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In their worthwhile Velocity talk on the need for API-based cloud configuration & control talks, Adam Jacob and Ezra make a crucial clarification that many industry sources (especially the marketing-based ones) don't understand: cloud computing is not cheaper per run hour - in fact, at current pricing, it's noticeably more expensive.
Where it saves you money is that it massively improves your time to market - it is the value of the weeks (buying your own hardware and getting it online) or days (using a traditional server host on the net, but still not the cloud per se) that you don't wait for your application to make it onto the net and start doing business.
(There can also be money saved from being able to dynamically scale to the level required by the load, rather than the worst-case scenario you can imagine - but this takes time to pay off.)
Their talk was well worth watching for a rundown of a few other important attitudes you need to adopt if you want to get real benefit out of cloud computing: