We used versions of SharePoint 2010 and 2013 before migrating to SP in Office 365. I can attest that adoption is a significant but not insurmountable hurdle with this otherwise great platform. We found that two factors made for increased use:
In terms of the broad adoption, however, constant promotion is required and high-demand content is essential. If there is a competing file share, make sure the critical content can only be accessed through the intranet. On that note, make sure there are no barriers to access, whether on premise or remote, using a mobile device, etc.
A popular component, from my experience, is a shout-out wall, where users can easily contribute a continuous stream of accolades and acknowledgements. Best case for this is enabling it for updates via instant messaging.
Finally, if you can get leadership to actively use - not just champion - the service, others will definitely follow!
Sharepoint can do just about anything you want, but it can't do it for free out of the box. If you are willing to invest some money and time you can create a really useful tool but don't expect to do it on the cheap.
Leland Foster, HM TE