Corrected - 7/17/2000 - Thanks bitter_engineer
The heat death of the universe is like global warming only worse. To paraphrase very roughly: eventually the temperature gradient of the universe will approach zero. When that happens, it will be impossible to do any work.
To quote the silly version of the three laws of thermodynamics:
you can't win
you can't break even
you can't get out of the game
Another possibility is that the universe will slow its expansion to the point that it begins to contract. What will happen then is not well understood, but it is likely that time will flow backwards and entropy will be reversed: ie a broken vase can jump off the floor and re-form itself.