One can easily find photos of galaxies colliding. You might think that this might make a mess like Central Expressway at 5:00, with collisions all around. This is not actually what happens; star collisions are in fact extremely rare. We'll explore how this actually could be.
Galaxies collide but stars don't. How so? What we need to look at is the ratio of distance between the objects to their physical size. Let's start with galaxies. The Milky and its nearest neighbor (Andromeda spiral) are about 100,000 light years in diameter (approximately). They are roughly 2,500,000 light years apart, which makes the ratio 25. Also - remember that such objects are very massive and attract each other gravitationally; they are in fact approaching each other now. They will collide long in our future. Look for photos of galaxy collisions - they do occur.
So how about Stars? What does the distance to size ratio look like here? To approach this we'll use the Sun as an example. We need to find out how its size compares to interstellar distances, which are measured in light-years (distance light tavels in one year).
The Sun's diameter is 1,393,540 km. The speed of light (c) is 300,000 km/sec. At this speed light takes 4.64 seconds to travel the Sun's diameter (1,393,540/300000). Now we need to know how many Sun diameters light will travel in one year. Take the number of seconds in one year (31,556,926) and divide that by 4.64 light-seconds per Sun to find 6,801,061 Suns in a light-year. In other words, light travels 6,801,926 Sun diameters in one year. Make note that nearest star (other than the Sun) lies about 4.25 Light-years away.
To make this understandable, let's make a model using something you can imagine - an NBA regulation basketball. The specification calls for a size of 9.5 inches, or 24.1 cm. This value (24.1 cm) is the diameter of our model Sun.
How many basketballs in a model light-year? Simply multiply 24.1 cm/Sun times 6,801,926 (Suns per light-year) and get 163,926,416 cm/light-year in our model. We'd like to have km instead of cm, so we divide by 100,000 to get 1,639.3 km for our model light year Or about 1016 miles).
Now imagine one basketball on a table here in Dallas. On that same scale another basketball representing the nearest star would be 4318 miles away, which is almost all the way to Dublin, Ireland! The interstellar distances are enormous compared to the sizes of stars. That's why the probability of collision is so tiny.
To get the distance to size ratio, first muliply 163,926,416 cm/light-year by 4.25 light-years (to nearest star) to get 696,687,268 cm as the distance to the nearest star. Now divide that by 24.1 (size of basketball Sun) and get a ratio of 28,908,185. Compare that to the ratio of 25 for the Milky way and Andromeda galaxies. See the difference?