The meaning of the word 'gay', for instance, began to change as early as 1870 among the criminal classes of New York, where it originally meant 'prostitute' (yes, before The Gay '90s) around 1900 the meaning changed to 'homosexual prostitute' and within five years of that to simply 'homosexual'. Keep in mind that some of these words actually did have their modern meaning at the time they were used, but only within certain sections of the populace. See also Double Entendre or Intentionally Awkward Title for when this trope is invoked entirely intentionally, Separated by a Common Language for the spatial analogue, and Get Thee to a Nunnery for the reverse process.
Compare with Hilarious in Hindsight, of which this is arguably a Sub-Trope.