What if two Galaxies collide?

If two galaxies collided, as our Milky Way galaxy and the nearest galaxy, Andromeda are predicted to do, nothing much will happen. Computer simulations have been run and the results generally show:

1. There will be few, if any collisions because of the vast distances between bodies in each galaxy,
2. There will be gravitational interactions which will redirect bodies, slightly or by a large amount, which will impact orbits, trajectories, and periods of orbits,
3. The galaxies will pass through each other and they will oscillate and pass through each other several times before finally merging.

After Effects of Galaxies Collision

1. They will merge into a larger galaxy. As space is a great big empty punctuated, here and there by stars, planets, dust, gas, comets, asteroids, et cetera, collisions are very unlikely. Some stars may be ejected from the galaxies during the interactions.
2. The Milky Way has merged with several smaller galaxies, and is currently in collision with the Sagittarius Dwarf Elliptical.
3. They would seriously disrupt the orbits of stars. They would then either continue on their way, but more likely revolve about each other, possibly colliding several times before settling down into a larger galaxy. 
4. There will be some gravitational interaction of the material in the two galaxies, but the chances of material from one galaxy colliding with material from the other is close to zero.

Well, these all points don't have some experimental reasons. These all points are results of computer simulations of Galaxy Collision shown below.

The End Notes

Generally nothing spectacular happens; in particular, the so called collisions of Galaxies occur over a long period of time, but there is a lot of pulls and pressures, tidal disruptions, star formation, etc. In some cases one galaxy may nearly disappear, most of its matter being absorbed by the other galaxy by gravitational pulls. These are all results from simulations. There is only sparse observational evidence as far as I know.