In a galaxy like the Milky Way, this is a very rare event over the age of the galaxy. The distances between stars are typically several light years. The diameters of stars are typically a million miles. This means that two stars have to be in orbits that are very carefully tuned so that the stars can suffer a collision. The impact rate is figured by multiplying the speed of the star as it moves, with the cross section of a star, and the density of stars in the galaxy; all in consistent units. Example, stars travel at a speed of 50 kilometers per second, they have a geometric cross section of pi x ( 1 million kilometers)squared or 3 trillion square kilometers. The density of stars in the solar neighborhood is about one in every 16 cubic light years or about 300 trillion trillion trillion cubic kilometers. Multiplying these together we get :
50 x 3 trillion / (300 trillion trillion trillion) seconds.
This means in order for one collision to take place, we would have to wait 2 trillion trillion seconds or 6,000 trillion years! So, the chances of any two stars in the solar neighborhood of colliding is very remote. There are, however, places where stars can travel at much faster speeds, and where there are far more stars per cubic light year that where we are located. In dense star clusters, or in the cores of galaxies, collisions between stars can be much more frequent and in fact there can be several of them over a period of billions or even millions of years.