Can orbital migration cause a planet to crash into the sun? If the planets move out of their current orbits into other orbits over long periods of time could this cause a planet to crash into the sun? Maybe the term crash is a little dramatic, could the orbit shrink to the point that the planet intersects with or is vectored into the sun?
Definitely. In the early solar system, there were probably several more planets than there are today. Gravitational interactions between the planets caused some to be flung into the sun, while others were sent spiralling into the sun until it settled out into the more or less stable configuration we have today. With the Kepler spacecraft and other exoplanet finding programs, we've come to realize just how big a factor migration can be. The best example of this is what are called 'hot Jupiters'. These are gas giant planets up to several times the mass of Jupiter that are in orbits that would be well within Mercury's orbit in our own solar system. These planets could not have formed where they are now, as when their parent stars ignited fusion they would have blown away all the gas in their immediate vicinity. This means that these planets must have migrated all the way in towards their sun. For each one we see in a stable orbit tight around its star or spiralling its way in, there were probably several more that collided with their parents. We just see the 'lucky' ones. 

Just to assuage any fears: This sort of thing mostly happens on such large scales in the first few million years of a solar system's history. A major migration isn't going to happen in our system. Our planets' orbits aren't entirely stable, but they'll last longer than the Sun will.