Oh yeah, it happens, and when it does it is truly a clash of the titans. Collisions are a major factor in shaping many of the galaxies we observe today, all the way from the more mundane (ha!) ellipticals to the very rare and extraordinary ring galaxies.
Don't worry though, we don't get left out the fun, it's going to happen to us too. Our beloved Milky Way and the closest (major) neighboring galaxy Andromeda are set to collide in a mere 3 Billion years or so. Now when galaxies interact like this there are rarely direct collisions between stars, however the gravitational forces often spawn rapid stints of star creation in a big way, literally lighting up the neighborhood.
In terms of observation from a distance, this means a pretty spectacular show - and this page at Galaxy Dynamics has some very interesting simulations that give us an idea of what it might look like when our turn comes around.