From The Black Hole at the Center of Our Galaxy, by Fulvio Melia:

The Milky Way and Andromeda, the two dominant spiral galaxies in our Local Group, are falling toward each other at 300,000 miles per hour. Our descendants eons from now will see Andromeda gradually grow in size until, some 3 billion years hence, the two sister galaxies begin to tear at each other's fringes. Eventually, stars from both doomed spirals will plunge past each other, driven by the gravitational force of the two gargantuan galaxies. The Sun itself, together with our planet, will either spin completely out of our galaxy altogether, traveling on a long, desolate path with very few other stars visible in the night sky, or it may plunge toward the center of the newly formed structure where a cacophony of activity will greet it. Since the Sun is expected to burn and sustain life on Earth for another 5 billion years, intelligent life here will see all of this unfold, albeit at a very slow pace. A billion years later, the two beautiful spiral galaxies will have merged into a giant elliptical spheroidal mass of aging stars. Ironically, though, very few stars will actually collide with each other during this encounter, since most of space is filled with wispy gas. Aside from dramatic changes in the appearance of the night sky, our descendants will continue to live on a planet peacefully orbiting around the Sun.

link (feeling lucky)