Mugs not being used

[God?]

My dwarves hardly ever use mugs and drink straight out of the barrels. Do I need to make actual goblets instead?

[Travis]

Mugs count as goblets. You can encourage dwarves to use them by placing chests or coffers in a tavern, which will store some goblets. Make sure drinks are nearby (ideally stored within the tavern) and they're much more likely to use goblets.

[Navi]

In my case, if they are inside a tavern they will not use them. I had to put them on a bin near the food stockpile

[Other]

Mugs assigned to a tavern CANNOT be used by thirsty dwarves. Those mugs are reserved for the Tavern Keeper and performer in the tavern (if you have assigned these positions, they will use those mugs to serve random tavern patrons on repeat, which will deal with getting booze into your dwarves). If you don't have enough mugs to go around, you can reduce the number your tavern has reserved, make more, or both. Mugs are one of the items that it can be best to never assign any stockpiles anywhere ever for them, since all that does is cause dwarves to waste time hauling them from the drinks room back to the trade goods pile