The milky-way and Andromeda galaxy are going to collide in about 7 billion years. Most of the stars in the galaxy will fly right past each other(a galaxy is mostly empty space). Lots of them will be thrown out into deep space. The super massive black hole in each galaxy will spiral inward towards each other creating a even larger super massive black hole. here are some videos about the impending collision

This one will give you a more in depth explanation
YouTube - Milky way vs. Andromeda
This one is just a graphic simulation
YouTube - Milky Way/Andromeda