"Significantly cheaper than doing this yourself, when you take into account the cost of building and maintaining a data centre, buying licensing."
Sorry but it's BS, typical of clueless MSFT marketing monkeys. People don't build DCs, they build server rooms, with one or two racks. As Trevor pointed out Azure's pricing is nonsensical when it's compared to a typical one rack cabinet worth of on-premise server, storage and networking stack including 3-y/4-hr support. If you have decent bargaining skills I can literally guarantee you will beat your comparable 3-y Azure quote at l;east by 50% if not more. And there are the usage details where cloud also fails: having 10GbE to the desktop is a no-brainer, costs very little extra nowadays (I run 10Gb to our WS for ~4 years now) - imagine your internet AND/OR your VDI bill when you want to do something similarly high-end in your cloud...
...did mention that anyone with existing infrastructure can get a huge discount after 3-4 year from any server or storage vendor?
The reality is that the pure cloud-base pitch makes clueless CEOs and alikes excited (mainly because they believe it'd save money for their bonuses but they are wrong) but most CIOs/CTOs know that beyond basic docs/email/web/etc usage it brings its own issues and when something happens you don't even have the hardware in your server room with your latest data on it.
I firmly believe hybrid cloud is the best pitch cloud providers can make and MSFT is YEAAARS behind... they should brought out integrated hybrid cloud offering with Server 2012, at least in 2012 clusters, with a one-click built-in Azure feature-set: mirrored cluster config in Azure, default DR, backup etc. It's almost 2015 and it's still not there and Ballmer was still stroking his idiotic tablet & devices plans - incompetency at its worst, they wasted years and billions chasing something they have little to do with while letting a huge market opportunity slowly disappear.