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.