sorcerer’s apprentice mode
n. A constant and uncontrollable flood of data, particularly one caused by an error where one message triggers multiple automatic messages, each of which triggers the same automatic response, and so on.
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So any time we make revolutionary changes, we are bound to see a great number of disrupting perturbations in the strangest and often unlikeliest of places. This example is also applicable (although it is not technology-related) to the societal convolutions that will result from the onrushing "data tsunami." Are we getting to the point where we are no longer in control of the spirits that we have invoked? Perhaps we are already in "sorcerer's apprentice mode" without being aware of it.
—Richard H. Nethe, “Mixed blessings: second thoughts on the information explosion,” The Humanist, September 01, 1996
1990 (earliest)
SORCEROR'S APPRENTICE MODE n. A bug in a protocol where, under some circumstances, the receipt of a message causes more than one message to be sent, each of which, when received, triggers the same bug. Used esp. of such behavior caused by BOUNCE MESSAGE loops in EMAIL software.
—Guy Steele, et al., “Jargon File,” MIT, June 12, 1990
This phrase is a reference to the memorable Sorcerer's Apprentice scene from the movie "Fantasia" in which Mickey Mouse, playing the eponymous hero, attempts to conjure up a broom helper, and ends up with an entire army of broom automatons.

On some email systems, you can set up an automatic reply for all incoming mail (often called a vacation message). Before doing this, however, you need to unsubscribe from or suspend all mailing list activities. That's because, in some rare cases, the automatic reply to a list message will get sent out to the entire list membership. Since you're a member of the list, you'll get your own reply, which will generate another automatic reply to the entire list, and so on until many teeth are gnashed and much hair is pulled.