The flag should be displayed on all days, especially on

New Year's Day - January 1
Inauguration Day - January 20
Martin Luther King Jr's Birthday - third Monday in January
Lincoln's Birthday - February 12
Washington's Birthday - third Monday in February
Easter Sunday - (variable)
Mother's Day - second Sunday in May
Armed Forces Day - third Saturday in May
Memorial Day (half-staff until noon) - last Monday in May
Flag Day - June 14
Independence Day - July 4
Labor Day - first Monday - September 1 - 7
Columbus Day - second Monday in October
Navy Day - October 27
Veterans Day - November 11
Thanksgiving Day - fourth Thursday in November
Christmas Day - December 25
Other days as may be proclaimed by the President of the United States
Birthdays of States (date of admission)
State holidays