As highlighted by Scott's Cheap Deals, the deals aren't all on the same airline. So, head to Google Flights to do a search like this one. (You can enter multiple destinations to see a variety of options.) SCD recommends you check the prices you find on Google flights against Momondo, where you'll find a slightly lower price on certain routes. For instance, the D.C. to Paris trip is $420 on Google Flights versus $401 through Momondo.
Other destinations worth looking into include Copenhagen (CPH), Florence (FLR), Geneva (GVA), Naples (NAP), Nice (NCE), Palermo (PMO), Stockholm (ARN), Warsaw (WAW), and Zurich (ZRH).
Cities that have dirt cheap flights, outside of the ones mentioned, include Austin ($525), Buffalo ($623), Calgary ($579), Charlotte ($405), Chicago ($525), Cincinnati ($431), Columbus ($511), Dayton, Denver ($613), Detroit ($466), Edmonton ($513), Fort Lauderdale ($402), Fort Myers ($526), Greenville ($398), Jacksonville ($550), Knoxville ($439), Las Vegas ($498), Los Angeles ($489), Lynchburg ($551), Miami ($430), Minneapolis/St. Paul ($431), New Orleans ($550), New York City ($431), Orlando ($509), Ottawa, Pittsburgh ($480), Philadelphia ($431), Phoenix ($550), Portland ($660), Richmond ($511), Saint John's ($459), San Francisco ($475), San Jose ($550), Seattle ($470), Tampa ($550), Toronto ($528), and Vancouver ($472).