The Big Rip is one proposed scenario for the end of the universe. If, as current astronomers have observed, the universe keeps expanding at an accelerating rate, which, bound by the laws of thermodynamics, as the universe continues to search for its state of more profitable entropy, it will continue to consume energy in the forms of its elementary self, cannibalizing its forces in order to grow. First gravity will cease to exist, then electromagnetic forces. Then the weak and strong nuclear forces. All subatomic particles will fly off into infinity, unable to communicate and interact with each other forever.

In the words of a great professor, "you might just be able to see your ass fly away."

This is expected to happen some 50 billion years in the future, and is effectively known as, the End of Time.

As the Big Rip is a relatively new concept in physics (proposed only in the year 2003), few fictional universes feature it such as Problem Sleuth (IE, DMK's Fill 'Em With Daylight), although causing/surviving one would be an incredible feats.

See also:

Big Bang
Big Crunch