There's a theory that our sun has a twin, aka another star that shares an orbit pattern with it (called Nemesis). We've yet to find it, but part of the theory is based on our assumption that a good percentage of stars come in 'pairs'.
The theory states this twin star is a dim red or brown dwarf that orbits every 26 million years. It's an absolutely fascinating theory to me, but I'm not sure how it's possible that we've yet to see this twin star, despite finding artifacts many light years away. Do you believe our sun has a twin?
There's a reasonable theory about our position within the galaxy causing higher risk for asteroid collisions every 26 million years or so. We are about 30,000 light years from the center of the milky way disk. The solar system oscillates between being "above" and "below" the disk due to gravity.
As we cross the plane of the disk every 26 million years or so, there are more stars in our path. While these don't normally come close enough to us to affect us directly, they are believed to cause objects within the Oort cloud at the edge of the solar system to change their orbit.
More comets appear in the inner solar system as a result. These may collide with planets, sometimes after wandering around in unstable orbits for thousands or even millions of years. The comet Shoemaker-Levy 9 which hit Jupiter is a good example of the types of collisions that happen. The rate of such events may be two or three times higher as we cross the disk.
This hypothesis is supported by a few scientists - most notably the late Gene Schoemaker, but there are problems with it.
PS - The period taken to traverse the galactic plane is around 30 million years, not 26.