As of March 2015, TSA rules permit coffee cups to pass through security with no more that 3.4 ounces of liquid inside; thermoses may be subject to additional scrutiny. TSA rules about bringing coffee on board flights may change over time depending on current intelligence about terrorist threats.
Insulated travel mugs are allowed on flights, but there may be additional inspection of them. Beverages purchased after security screening may be brought on board the flight, such as those in standard Starbucks paper coffee cups. Empty coffee cups may also be brought on board and then filled with coffee during the flight if so desired.