Collision of Andromeda and the Milky Way
Almost all galaxies are moving away from us because of the
Hubble expansion of the Universe.
However,
some nearby galaxies can actually move toward us because of local motion over and
above that associated with the expansion of the Universe (this motion is called
peculiar motion). One such example of peculiar motion is that the
Andromeda Galaxy (adjacent image)
is moving toward us and it appears that Andromeda and
the Milky Way will collide in about 3 billion years.
Here is a
simulation
of the collision
(Source).