Is there a website similar to FlightRadar24, but showing general aviation?
Yes, and no.
FlightAware (and I believe FlightRadar24) will show General Aviation aircraft (I panned around a bit and found N802AF, a Pilatus, buzzing around over Bethlehem, Pennsylvania just now).

The catch is most of these systems are fed with ATC data, and generally only pick up flights that are either on an instrument flight plan, or which have picked up flight following &amp; been entered into the ATC system by the controller who set up the strip.  

Most light GA aircraft are flying around VFR (transponder code 1200), and don't show up on these flight tracking sites. Similarly if you're assigned a "local" transponder code rather than a system-wide one  you typically won't show up on the tracking sites either (this is often the case when you're flying VFR and go through Approach/Departure for Class C or Class B transitions/arrivals).



As more of the fleet is equipped with ADS-B this coverage may improve, as anyone can set up an ADS-B receiver and skim the traffic data. That data is currently only broadcast when a "participating aircraft" (ADS-B Out equipped) is in the area though...