Most movies depict a few days to a week's worth of real-time. What movie depicts the longest amount of time?
Although the fantastical plots of TV shows like Dr. Who and Futurama might trump it, The Tree of Life from 2011 must be a serious cinematic contender. Its story spans the beginning of the universe until present day (showing us along the way the big bang, the creation of the solar system and the extinction of the dinosaurs), which means approximately 13.8 billion years.
However, near the end of the movie this happens:
In the present, adult Jack leaves work. Riding the elevator up, he experiences a vision of following a young girl across rocky terrain. Jack tentatively walks through a wooden door frame erected on the rocks and sees a view of the far distant future in which the sun expands into a red giant, engulfing the earth and then shrinking into a feeble white dwarf.
The ending is open to interpretation, but if we take Jack's vision at face value, then this would add around 6 billion more years to the tally (which is when it's estimated that the sun will become a red giant). This would mean that The Tree of Life spans around 20 billion years and covers all of our existence.
The winner would probably be "The Hitchiker's Guide to the Galaxy" from 2005.
At the end of the movie, we see the main characters travel from (approximately) the present day to the Restaurant at the End of the Universe, a span of some 1010120 years into the future.