How long can cookies sit out at room temperature?

It depends on the cookie. Dry cookies aren't likely to attract spoilage bacteria (the kind that won’t make you sick, but may  spoil the taste and/or smell of the product), but they will eventually grow hard.
 
However, cookies with high moisture and oil content are more likely to attract spoilage bacteria  or grow rancid. They should be stored in plastic wrap or an airtight lidded container within two hours.
 
Source(s):
Canadian Food Inspection Agency "Food Safety Facts on Leftovers"