I think the biggest direct competitors are Rackspace, Windows Azure, Google Cloud, HP, and Dell. Indirectly, VMware and OpenStack are huge competitors too. Lots of companies are trying to decide how their existing infrastructure fits in with cloud computing, and the "private cloud" is one likely choice.
None of these have the wide product functionality that AWS has -- yet. Amazon has a multi-year head start on most of these companies, but as you mention, there's lots of time to make progress before 2020.