The Milky Way has not had a major collision for about ten billion years. We know this because major collisions scramble galaxy disks, and the Milky Way's disk has some very old stars.
Minor collisions happen all the time.
The Milky Way is now colliding with a very small galaxy, the Sagittarius dwarf. The Milky Way is on a collision course with the Andromeda Galaxy. In about ten billion years the two galaxies will merge and a single elliptical galaxy will form.