Answer:

BARTABS

Answer	Crossword Clue
BARTABS	Drinkers may run them
BARTABS	They might be run up
BARTABS	Tavern IOUs

BARTABS	Checks for drinks
BARTABS	Tavern tallies
BARTABS	Bills for drinks
BARTABS	Checks in "Cheers"
BARTABS	Grasshoppers can help make them
BARTABS	Drinkers may run them up
BARTABS	What some drinkers run up
BARTABS	They may be running in a saloon

BARTABS	Saloon patrons' running totals
BARTABS	They're used for tracking shots
BARTABS	Things with round numbers?