http://en.wikipedia.org/wiki/Andromeda%E2%80%93Milky_Way_collision
Each galaxy contains over a hundred billion stars, which is 100 million trillion possible collisions. Nevertheless, the chance of even two stars colliding is negligible because of the huge distances between them. For example, the nearest star to the Sun is Proxima Centauri, about thirty million solar diameters away. If the sun were a ping-pong ball in Paris, the equivalent Proxima would be a pea-sized ball in Berlin (and our galaxy would be 12 million miles wide—about a third of the distance to Mars).
Stars are much denser near the galactic centers—the average separation is only 100 billion miles. But that is still a density which is about equal to one ping-pong ball every two miles. Thus, it is extremely unlikely that any two stars may collide, and the two galaxies would swirl through each other like two clouds.
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