late 14c., "aspire or plan maliciously, agree together to commit a criminal or reprehensible act," from Old French conspirer (14c.), from Latin conspirare "to agree, unite, plot," literally "to breathe together," from assimilated form of com "with, together" (see con-) + spirare "to breathe" (see spirit (n.)), perhaps on the notion of "to agree (by spoken oath) to commit a bad act." Or perhaps the notion is "to blow together" musical instruments, i.e., "to sound in unison."
Neutral or good sense of "to contribute jointly to a certain result" is from 1530s. Related: Conspired; conspiring.