user17920: What was the first chess engine that could beat the world chess champion when running on a standard desktop playing at standard speeds (i.e. not blitz chess)? For concreteness, say a $1000 PC.

user12873: A standard desktop today is significantly more powerful than whatever machine Deep Blue was running on in the mid-1990s against Kasparov. Since Deep Blue was the first engine to beat  a world champion, that's the answer to your question.
Note that there may have been an engine before Deep Blue that, if it ran on a modern day desktop, could have beat Kasparov. But we never saw such a match happen so it's just speculation to say any earlier engine than Deep Blue.

user825: Deep Blue was a super computer. In the 2006 match, Kramnik was defeated by Deep Fritz that everybody could buy.

In a November 2006 match between Deep Fritz and world chess champion
  Vladimir Kramnik, the program ran on a computer system containing a
  dual-core Intel Xeon 5160 CPU, capable of evaluating only 8 million
  positions per second, but searching to an average depth of 17 to 18
  plies in the middlegame thanks to heuristics; it won 4–2.[31][32]  

(source)

17920: <p>What was the first chess engine that could beat the world chess champion when running on a standard desktop playing at standard speeds (i.e. not blitz chess)? For concreteness, say a $1000 PC.</p>
 12873: <p>A standard desktop today is significantly more powerful than whatever machine Deep Blue was running on in the mid-1990s against Kasparov. Since Deep Blue was the first engine to beat  a world champion, that's the answer to your question.</p>

<p>Note that there may have been an engine before Deep Blue that, if it ran on a modern day desktop, <em>could</em> have beat Kasparov. But we never saw such a match happen so it's just speculation to say any earlier engine than Deep Blue.</p>
 825: <p><a href="https://en.wikipedia.org/wiki/Deep_Blue_(chess_computer)" rel="nofollow noreferrer">Deep Blue</a> was a super computer. In the 2006 match, Kramnik was defeated by <a href="https://en.wikipedia.org/wiki/Fritz_(chess)" rel="nofollow noreferrer">Deep Fritz</a> that everybody could buy.</p>

<blockquote>
  <p>In a November 2006 match between Deep Fritz and world chess champion
  Vladimir Kramnik, the program ran on a computer system containing a
  dual-core Intel Xeon 5160 CPU, capable of evaluating only 8 million
  positions per second, but searching to an average depth of 17 to 18
  plies in the middlegame thanks to heuristics; it won 4–2.[31][32]  </p>
</blockquote>

<p><sup>(<a href="http://www.chessgames.com/perl/chess.pl?tid=54499" rel="nofollow noreferrer">source</a>)</sup></p>
