What if the Earth just stopped dead in its tracks while orbiting the Sun? It would plummet straight down of course, but how long would it take to actually crash into the Sun?

Ask an Astronomer article: http://curious.astro.cornell.edu/about-us/39-our-solar-system/the-earth/other-catastrophes/57-how-long-would-it-take-the-earth-to-fall-into-the-sun-intermediate
Wired article: http://www.wired.com/2014/12/empzeal-earthfall/