In S1E2, when Lorelai and Rory arrive at Chilton on Rory’s first day, they both sit in the car staring at the school in awe. Rory finally says, “I remember it being smaller,” to which Lorelai replies, “Yeah! And less…” “Off with their heads,” finishes Rory. “Yeah!”
“Off with their heads” is so common now that it doesn’t necessarily need to refer to a specific historical usage, but it probably originated with Shakespeare. In Shakespeare’s play “King Henry VI,” Queen Margaret exclaims, “Off with his head, and set it on York gates; so York may overlook the town of York” (the man whose head was to be “off” was named York).
Lewis Carroll’s “Alice in Wonderland” also features the phrase “off with his head,” uttered by the tyrannical Queen of Hearts.