People are great at seeing patterns, it's one of the things we do really well. But sometimes were too good, and we see patterns that aren't there. For example, we see faces everywhere we look. Just Google image search "ghosts" and you'll see a whole bunch of shadows that are interpreted as faces (as well as photoshopped images). Another good example of this is the well-known face on Mars, which is just a plateau that was photographed at a convenient time, the face was in the shadows, not the planet.
An example given in the Bad Science piece is "runs", and why random patterns can look decidedly nonrandom. He gives a specific experiment that demonstrates this effect, but there's another well-known one. If you've taken a class in or read any material on probability theory, you've probably heard this story. It goes that a Professor of a large introductory probability class gives an odd assignment the first day of class: half the class flips a coin 100 times and records the result, while the other half just makes up data. He goes through the results and can separate most of the people who made up data from those who didn't.
How would this be done? As it turns out, people hate putting down long strings of the same result, but in a large data set they're virtually guaranteed to occur. So the results that contain strings of 6 or so in a row are usually real, and those that don't aren't. Of course, this is probabilistic, it doesn't always work, but it does with pretty good probability.
Not only are people horrible at creating random patterns, we're just as bad at making random numbers. Some folks over at Scienceblogs (specifically Cognitive Daily) did an experiment to demonstrate this, and it has been verified by others in the science blogging community.
The result is that if you ask people, 17 is the most random number (between 1 and 20 anyway). I guess it "feels" more random, whatever that means.
I think this can be generalized even further, in that we really like for there to be patterns behind things, for events to have causes that aren't random. Einstein famously said, "God doesn't play dice" in voicing his opposition to Quantum Theory, but indeed, the universe is probabilistic, whether we like it or not (according to a new study, nature might be even weirder).
This is why, I think, we have such a hard time accepting that certain events were random. People still think that the Kennedy Assassination was a conspiracy theory, despite thorough debunking of all conspirator's claims (see, for example, Penn & Teller's episode of Bullshit! on it). I'd even go so far as to say it's behind the reactions to the VT massacre earlier this week (at least those not obviously motivated by grinding axes), and the seemingly universal desire to believe that there's a greater cause driving the world, that things happen for a reason.
We see patterns everywhere, and so they must be everywhere. It's too bad that sometimes the world just is random, and we have to learn to deal with that.