Wired recently published an excellent article on Turing's Halting Problem (including the humorous poem SCOOPING THE LOOP SNOOPER that describes it). As Aatish Bhatia says: "Computers can drive cars, land a rover on Mars, and beat humans at Jeopardy. But do you ever wonder if there's anything that a computer can never do?" Well there is - solve the Halting Problem.
from The Universal Machine http://universal-machine.blogspot.com/