Bruce Schneier has linked to an interesting story about how Michael Larsen, a contestant on Press Your Luck memorized the possible pseudorandom sequences (there were only 6 at the time), and used that knowledge to win himself over $100,000 and vacation prizes. Another account of that story is here, at a site that also hosts a number of compressed clips of the show, including the episode in question.
In retrospect, I'm only surprised that it didn't happen sooner. Perhaps it did, only with nobody noticing, because the contestants weren't as greedy. I only watched that show when I was a child, but even as a child, I remember being caught by the fact that I was sure that I had seen an exact pattern of motion repeat itself, and started playing a game-within-a-game (because even as a child, I found the program somewhat boring): see if I could arrange it so that I could tap a piece of paper before every contestant, and never tap a whammy. I wasn't as ambitious as Michael Larsen, not aiming specifically for Spin Again squares or memorizing exact movement sequences, but I had a methodology where I had memorized the patterns of movement from side to side, and the patterns of when whammies appeared on each side, and did exceedingly well playing against myself with my piece of paper.
Then I stopped watching television so much, grew up, and by the time I was old enough to understand pseudo-random number generators or get on a gameshow if I wanted to, I had forgotten all about it. The patterns were harder by then anyway: immediately after Michael Larsen made off with his winnings, the show producers added sixteen more pseudorandom sequences, making the game much harder to predict. Just in time, too: the very next contestants on the show had also figured out the older patterns.
That wasn't the only game show I had gamed as a child. I remember being able to predict with quite some regularity what the next few spins of the wheel would provide on Wheel of Fortune; it turned out that many players had a very regular pull, and would always pull within a couple tags of a complete revolution... and consistently, exactly that many tags shy under or over on every spin. Why none of them noticed that, and pulled harder or lighter deliberately to avoid the inevitable Bankrupt tag heading their way, I don't know. That's more a problem with direct human control over placement than with pseudo-randomness, though.
Game shows aren't the only places with real problems with pseudorandom generators. I remember an old story about people hired by casinos and trained specifically to know the sequences before big hits on their slot machines, so they could trigger them and return the winnings to the casino before any random visitor would have the chance.
And then of course there are the slew of current technological marvels, the security of which depends upon unpredictability, and fails sometimes when that unpredictability, isn't. Recent attacks on TCP sequence numbers come to mind, among other things. These issues have been mostly solved, now, but I expect that examples will keep cropping up for quite some time, particularly in developing countries.
