A better phrasing would be that they "fall into each other."
We are currently falling around the sun. The gravity between the earth and the sun, along with the perpendicular motion to that force of the earth moving along on it's orbit is what keeps us from falling into the sun.
If, for whatever reason, the earth slowed down significantly in it's orbital speed, it would fall closer to the sun, or even into it. If, for some reason, the earth sped up significantly, it would have enough velocity to escape orbit.
What remains in our solar system makes "collisions" very rare, for it is old enough for most unstable orbits to have already "crashed" or have already "escaped" by now. But gravitational perturbations still occur. It wasn't long ago when Comet Shoemaker-Levy 9 fell into Jupiter.
In young and forming solar systems, which much debris and less established orbits, this happens frequently. Look at the craters on Mercury or the moon. Those are visual remnants of astronomical bodies colliding in the past. Although in most of those cases, the impactors were not anywhere near the mass involved with a "planet" or a "star" as your question indicates.
But look up the current theory on the formation of the moon. Very likely a planetary "crash."
Star collisions are much less likely. Even when two galaxies collide / merge, the amount of space between the stars is great. And collisions are rare, but not impossible.