The Black Plague (also called the Bubonic Plague, or Black Death) decimated medieval Europe back in the mid 1300s. Estimates run up to 200 million dead, which is a lot for the mid 1300s. (It was caused by a bacillus, carried by fleas, which came on rats, which arrived on boats. It was perhaps the nastiest thing ever to hit human-kind.
So naturally, it was something you should completely avoid.
Dijkstra wrote that back in the 50s [more or less]. Unfortunately, since then, it has become an overworked cliche - a phrase that has seen better days.
One set of the Rules Of Grammar has "Avoid cliches like the plague".
I don't think he meant that clever tricks were like the plague, but rather, that you should not use "clever tricks" at all. Clever tricks, in programming, will almost cause terrible headaches for people who have to update the program later on.