When is a flight plan required?
In the US you need to file a flight plan for the following flights:


IFR flights
Defense VFR Flights, which are required to fly in the ADIZ that is off the coast of the US (an IFR flight plan may also be used).
Some TFR's only allow air traffic to fly within their boundaries if they are on an IFR or VFR flight plan.
A DC FRZ flight plan is required to fly VFR in the DC FRZ.
A DC SFRA flight plan is required to fly VFR in the DC SFRA.
When entering or leaving the U.S., an ICAO international flight plan (IFR or VFR).


Other than that, no flight plans are required, but are strongly recommended so that search and rescue gets called if you don't show up at your destination on time!