Ettus Research, creators of the high end USRP software defined radios have posted a well produced video on YouTube showing off various applications that an SDR can perform. In the video they go through and explain FM Radio, APRS, AIS, Multi-Channel Decoding, Pagers, ADS-B/Mode S, ACARS, RADAR Analysis and 802.11a decoding.
For these apps they use a USRP B200, which costs $675 USD. Most of the applications shown should also be compatible with other SDRs, such as the cheaper HackRF and BladeRFs. Even the cheap RTL-SDR will at least work for FM Radio, APRS, AIS, Pagers, ADS-B and ACARS. Of course, the USRP is still probably the most top of the line SDR available.
Update: The video creator, Balint has also uploaded a video on his personal YouTube channel which is a longer presentation of the topics that were briefly discussed in the USRP video.