Nintendo will probably make an announcement at E3 this summer about the launch date. Historically, Nintendo has announced new consoles the year prior to release, but there are many rumours that point to a 2016 launch. Nintendo has traditionally launched home consoles in November (Nov. 18, 2001 for the Gamecube, Nov. 19, 2006 for the Wii; Nov. 18, 2012 for the Wii U). Given this, it is reasonable to expect to see the NX in November 2016.
However, the NX may be a combined handheld and home console, with the two components sold individually. The 3DS is getting pretty old now, and it would not surprise me if Nintendo released the handheld portion first. The company is not as predictable with handheld console launches. The DS followed normal practice and launched in November, but the 3DS bucked that trend and was released in February/March 2011 after being announced at E3 2010.
My take on all this is that we will NOT see both the handheld and home console parts/versions of the NX released this year. The poor sales of the Wii U make it likely that it will be replaced before the 3DS, but I'm still not entirely convinced of a 2016 launch. I think it's likely, but it would be more in line with Nintendo's history to announce at E3 in June 2016, launch the handheld portion either in November 2016 or March 2017, and launch the home console in November 2017.