First published on MSDN on Jun 13, 2016
UPDATE: Corrections/clarifications were made on 7/12/2016. Thanks for the comments!
It's come up in the last few days where people want to know if SharePoint 2013 will support SQL Server 2016. (support as in store all SP's DB in...) The answer to this question is no, SharePoint 2013 will never be supported on SQL 2016. (with the exception of SSRS integration, keep reading for that) SQL and SharePoint support generally works in the following way. A SharePoint release will support the latest SQL Server version(n) at the time of release as well as the one previous released version (n-1) and one addition/new release of SQL (n+1). For the case of SharePoint 2013, the follow SQL versions are supported:
SQL 2014 - n+1
SQL 2012 - n
SQL 2008 R2 - n-1
If we want to expand this list to SP 2016, we can assume we'll support the following
SQL Server Reporting Services Integration rules
The part of this discussion that gets a little confusing is SQL Server Reporting Service (SSRS) integration. Since SP is just using the SSRS add-in to render reports, the supportability matrix does expand some. In the table in the link below, we can see that you can integrate SSRS 2016 with SP2013 via the SSRS2016 add in.