Here is a wonderful image of two galaxies in the midst of a million-year-plus long collision.
From NASA's image of the day description:
"This interacting pair of galaxies is included in Arp's catalog of peculiar galaxies as number 148. Arp 148 is the staggering aftermath of an encounter between two galaxies, resulting in a ring-shaped galaxy and a long-tailed companion. The collision between the two parent galaxies produced a shockwave effect that first drew matter into the center and then caused it to propagate outwards in a ring. The elongated companion perpendicular to the ring suggests that Arp 148 is a unique snapshot of an ongoing collision."
It's worth noting that our galaxy and Andromeda will be doing this kind of dance in a few billion years (start worrying now, its never too early.)