We have several customers taking a cloud-first approach to core infrastructure services, it depends on the level of confidence they have in their service providers (including us). Some of them are so cloud-focused they are even buying cloud-managed networking/wireless/security and getting someone else to manage that for them as well. We've got a lot of businesses on our hosted Lync service and have had great results and growth in that area. Putting VoIP in the cloud is a big commitment, but it seems to be working out well.
A lot of it boils down to cost. I can put 10 medium instances of Windows Server or RHEL in our cloud for 5 years for less than the cost of a single server with local disks (never mind licensing etc). Since most of our smaller customers are running less than 10 distinct workloads (and simply using hosted services for common workloads like email and the aforementioned collaboration), many of them don't even bother with a server at all.