Our galaxy, the Milky Way, is a collection of about 400 billions stars spread out in a thin disk more than 100,000 light year across. Our Sun, the center of the solar system, is one of those stars sitting about midway out in the disk moving around with the others on nearly circular orbits. The Milky Way would look like one of the most spiral galaxies if we could see it from the outside - nothing special.
The nearest big spiral galaxy is the Andromeda galaxy, in the direction of constellation Andromeda. It is about twice as big as the Milky Way, but very similar in many ways. At the moment, it is about 2.2 million light years away from our solar system but the gap is closing at about 500,000 km/hour. The reason is that the 2 galaxies formed close to each other, shortly afther the Big Bang, and they are a bound pair in orbit of one another. From one point of view, they seem to fall into each other, instead moving apart with the overall expansion of the Universe.
Galaxies collide and interact occasionally and there are several well-known examples in the vicinity of the Milky Way - they can be seen by the telescopes (as Hubble space telescope) and studied by the scientists. The results are often very dramatic: long streams of stars thrown off in beautiful open spiral patterns are characteristic of these collisions and are known as tidal tails and bridges because of their origin in the strong mutual gravitational tides of the two interacting galaxies.
The simulations made by the scientists revealed a tremendous amount of detail in the destruction and unravelling of the galaxies as they collide and merge to form an elliptical galaxy. The Milky Way is shown face-on and moves from the bottom up to the left of Andromeda and the to the upper right. Andromeda is tilted from this perspective. As you can see in the video, after the initial collision an open spiral pattern is excited in the both the Milky Way and Andromeda and long tidal tails and a connecting bridge of stars form are apparent. The galaxies move apart and then fall back together for a second collision and then after a few convulsions which throw off more stars in complex ripple patterns they settle into something looking like an elliptical galaxy. The images are 1 million light years across.
It is uncertain what will happen with our solar system and Earth. It's a great chance what the Sun and all the planets in the system will die before the collision, but also there are chances that the solar system will be ejected from our current galaxy (the Milky Way) and it will not be a part of the new galaxy.
