Is there a free program, preferably executable, that allow me to play Quoridor against an AI? There isn't a publicly available one for the Zillions engine, even if it doesn't seem that hard to write one, despite workarounds being required. Programming the game has already been the subject of academic papers (here and here) and a university course (here).
I made an AI agent playing Quoridor. You can play against it right on the browser here: https://gorisanson.github.io/quoridor-ai/. As you can read on the "about" section on the page, I imitated the demonstration model of Daniel Borowski's Quoridor AI (https://danielborowski.github.io/site/quoridor-ai/display.html).
Martijn van Steenbergen's Quoridor program source code in Java (which maybe had been on the link https://code.google.com/p/quoridorai/ of Tom Wilkinson's answer) is now available on https://github.com/MedeaMelana/quoridorai. When I compiled the source code by Java 8 (JDK), it ran well.
Xoridor is available as a .jar file that will run wherever you have a Java installed and supports 2 or 4 players.
This version (mentioned in a comment): http://danielborowski.com/quoridor-ai/display.html is the first hit on Google and works in browser but only seems to be two player. I beat it on my first attempt but I'm used to 4 player games. Since the code is on GitHub you could probably extend it to 4 players.
I also found this link here: http://becool.info.ucl.ac.be/aigames/quoridor2013 That has been coded in python.
There's also this in Java: https://code.google.com/p/quoridorai/