Planetary systems become unstable when the orbits of two planets cross.  By this I don't mean that the planets collide, rather, that their crossing orbits cause them to have a close gravitational encounter.  The close gravitational encounter can transfer a tremendous amount of orbital energy from one planet to the other, potentially shooting it out of the planetary system.

 

Surprisingly, our own system is barely stable!  A close encounter between the asteroids Vesta and Ceres in about 60 million years ago makes it very difficult to trace Solar system dynamics before the encounter (http://www.sciencedaily.com/releases/2011/07/110715135156.htm) and also limits our ability to forward-predict Solar System dynamics on timescales longer than about 10 million years.  For more information about the stability of the Solar system, see this Wikipedia article and its sources: http://en.wikipedia.org/wiki/Stability_of_the_Solar_System

 

In summary, to make the Earth a "rogue planet," the Solar system would have to evolve such that another large body (a large asteroid, or Venus or Mars, or eventually Jupiter) crossed orbits with the Earth.  The asteroids and Mars probably don't have enough energy to eject Earth.  A more massive planet like Jupiter would be more effective at ejecting Earth, but Jupiter is quite far away and is less likely to cross orbits with Earth.  But the Solar system is definitely stable for the durations of our lives, and this kind of ejection couldn't happen for at least a few tens of millions of years, if not billions.