In September 2017, Microsoft announced the availability of Feature Pack 2 for SharePoint Server 2016. This update includes initial support for the SharePoint Framework-based customizations in locally hosted SharePoint 2016 farms.
The update is available through the September 2017 Public Update, and the bits can be downloaded for your SharePoint 2016 farm from https://technet.microsoft.com/en-us/library/mt715807%28v=office.16%29.aspx.
As the support does not--at least in the initial release--have parity with all the SharePoint Framework functionalities Microsoft supports with SharePoint Online, it is more limited but still very usable. Now, developers can target their code for on-premises and cloud-based deployments, with minimal, if any, changes to their code. In time, Microsoft will provide further updates to SharePoint 2016, which makes using SPFx a logical choice as a development approach.
Customers who are still running older versions...