Not that we'll ever live so long as to see one with the Milky Way...

Odds are, the two colliding galaxies would simply pass through each other, with mild stellar and planetary system perturbation. The oddity would therefore be when a galaxy eats another galaxy. We have some possible samples available via Hubble for this phenomenon, but also a local view. The Large and Small Magellanic Clouds are two arms that used to form a single spiral galaxy in their own right, and are now apparently the aftermath of the Milky Way's last big supper.

...What a glorious sight that must have been...

The Milky Way Also has multiple black holes at its core, the number of which might even be a count of galaxies devoured, or otherwise disrupted.