I don't know if Gartner coined the term "cloud computing," but they are certainly staking their claim for having some thought-leadership in the space (and who can blame them).
According to a press release, "Gartner defines cloud computing as a style of computing where massively scalable IT-related capabilities are provided 'as a service' using internet technologies to multiple external customers."
Which, as far as I'm concerned, is what software as a service (SaaS) does, too. Indeed it's what application service providers (ASPs) did, as well, but let's not even go there.
Source: Business Review, http://www.businessreviewonline.com