From a really cool timeline at
pbs.org, based on recent discoveries that not only is the universe expanding, but it's also accelerating in its expansion due to '
vacuum energy'...
3,000,000,000 years in the future, the Milky Way will collide with the Andromeda Galaxy, either combining into one large galaxy, or ripping each other apart.
100,000,000,000 years from now, galaxies that aren't gravitationally bound will start to disappear... that is, they'll be so far away, we won't be able to see them. Of course, the sun will have burned out by then and the Earth will be gone, but still...
At 1,000,000,000,000 years, the last of the stars will have burned out, ending the Stellar Era we're currently in. The Stellar Era gives way to the "longer, lingering death for our Universe." known as the Degenerate Era.
The Degenerate Era lasts until... hold on, let me make sure there are enough zeros... 10,000,000,000,000,000,000,000,000,000,000,000,000 years from now. The only energy remaining will be in the form of proton decay and particle annihilation.
Energy continues to dissipate until (Scientific Notation used for clarity) 10^100 years (nice round numbers, huh?). At this point, the Dark Era begins. Black holes will have completely evaporated, and the only remnants of the Universe will be "neutrinos, electrons, positrons, and photons of enormous wavelengths."
Creepy, huh?