Kayak does this when looking for flights. The results are instant, but by taking more time, it's giving the impression that it's trying really hard.
Relevant discussion on the UX Stack Exchange: http://ux.stackexchange.com/questions/41682/pros-cons-of-spl... (which also links back to a story on HN about a locksmith.)
That sounds a bit like the cake mix people who discovered that they got better sales if the mix required an egg to be broken and beaten into the mix. The taste was no different, but the cooks felt better. Or the antiseptic spray that added a component to give the sting consumers expected.
An engineer of elevator systems would spend hours doing all his calculations by hand, vowing it was too complicated and important to trust to a computer. (Yeah.)
The programmers in the company assured him they could write a program to do the calculations for him, which they did. He never trusted the results though, insisting that the program was not producing correct results.
One of the programmers realised that he didn't trust it because the program spat out the results almost instantly. It was too fast, it had to be wrong.
So he stuck a twenty second sleep in before the output, told the engineer he found the problem and fixed it. The engineer now felt the results were correct.
(Aside: I don't think I would want to get in a lift designed by an engineer who intuits the correctness rather than verifying the math, but I thought it was an interesting little parable on user interface design.)