As an aviation enthusiast, I've got a Raspberry Pi in my attic hooked up to two RTL-SDR radios, each connected to homemade antennas mounted on my roof (one VHF to listen to airband transmissions and the other receiving ADS-B[1]). No signal processing required--both are pretty easily achieved by just cobbling together existing open source packages. Also have a GPS receiver on the roof so that Raspberry Pi is also a stratum-1 NTP time server[2]. But that one's not using an SDR. Fun hobby.

EDIT: Added links I found helpful, for the curious:

1: http://www.rtl-sdr.com/adsb-aircraft-radar-with-rtl-sdr/

2: http://www.satsignal.eu/ntp/Raspberry-Pi-NTP.html