The Mug Incident was the revelation that the fortress had accidentally produced hundreds upon hundreds of mugs from every conceivable material available on fortress grounds at one point or another. It was discovered during another overseer's term after they noticed just how bad the mug situation had become.
At the time the mugs were just a temporary clutter clearing measure enacted during the first year of the fortress' life. However, the order had stood at "Continue production" with no specified orders to cease after a period of time.
Mugs, once considered the bane of the fortress are now its chief export. Chances are if you live in the northern-most Coastal Reaches during the time of the fortress, your drink your water or brew from a Spearbreakers mug.
Mugs became so ingrained in the fortress that it's not considered normal anymore unless there's a ridiculous amount on hand. At present the current number outstrips the number of things that have died on fortress grounds by several orders of magnitude, to say nothing of how badly they outnumber the dwarves. They are so prolific that sum have considered making weapons out of them and they are sometimes even used as currency in the fortress, with a good meal being two mugs and a mug of booze being worth three smaller empty mugs. Metal ones are sometimes used for gambling.
It is unknown if these are actual prices or just a joke, but that's the story that was given to several groups of migrants.