Most see IaaS as Infrastructure as a Service and it certainly is that. Another "I" would be Integration as a Service aka IPaaS or Integration Platform as a Service.
We know the former IaaS players, they are Amazon, Rackspace, OpSource, IBM and ProfitBricks. They sell computing power as a service, they typically call that service "The Cloud" because they are using some form of virtualization.
The second form, of Integration as a Service includes a smaller set of players including Mulesoft with their CloudHub, and QlogicTek, SOA Software that offer prebuilt Application Integration Services as a Subscription service.
Several Software as a Service vendors like SalesForce.com offer some Integration capabilities via their API and SDK, but don't offer the IaaS separately.
Same is true for the PaaS vendors, like WorkXpress, Heroku, and Engine Yard also have some capabilities for Integration but don't offer the Integration as a Service separately.
There is a very small list that offers solutions that cover all of the above. Software as a Service (SaaS) with business applications as a subscription services, plus Development and Deployment capabilities for Platform as a Service (PaaS), plus Infrastructure as a Service (IaaS) for processing power as a service, pluse Integration as a Service (IaaS or iPaaS) for Application Integration. That list includes @O4BO and you can subscribe to any ONE of those SaaS or PaaS or IaaS or iPaaS independent of the others.