One of the more challenging adoption issues has been that by default version control is turned OFF in SharePoint. When we do audits of our clients SharePoint environments, we see very weak adoption of version control simply because most site owners cannot find the setting and don’t remember to turn it on when a new site is provisioned.
Microsoft has now changed this setting in SharePoint Online / Office 365 so that versioning is now turned on by default for any newly created site. The versioning turned on is set to Major versioning which in most cases is sufficient for many users. Site owners with sufficient privileges can still turn off version control
The only negative impact to turning on version control is increasing the amount of space being taken up by versions of documents. However, in my experience the benefits typically outweigh the space impacts by ensuring the history of changes to documents are preserved.