14% - 2012 House Elections
The best source of information on US voting behavior is definitely the American National Election Survey. A single slice of their data easily captures hundreds of variables. They utilize a weighted sampling design and panel studies to comprehensively cover the public. What I'm saying is - it's a good study.
The 2016 data isn't available yet, so I downloaded the 2012 data. To answer the question, I focused on the 2012 House of Representatives elections. Variables for other races are available. I excluded people who either were not registered with a party*, or did not vote in this race.
In that election, 86% of Democrats and Republicans voted for the candidate from their own party. The remaining 14% voted for other parties. These percentages were similar for both Democrats and Republicans. In both cases, about 1% voted for independent candidates.
It's worth noting that only 31 states ask voters to register as a member of a party. As such, the data is limited to those 31 states. Because of this difficulty, I did not calculate variance or error values for the percentages above.
Only registered Democrats vote in Democratic primaries
this is not true in all states. Some states allow voters not affiliated with a party to vote in any party's primary.