Mostly it's just fun. I like peeking at all the ambient transmissions in the area.
A while back I was more deeply involved in the SDR space and even reverse-engineered some pager signals. At least a few years ago, pagers were still widely used in hospitals (totally in plaintext, by the way).
The RTL SDR is the gateway drug into SDR's. The bandwidth is limited, so don't expect to be capturing HDTV Streams. But it's certainly possible to listen to AM/FM, Ham Bands, VHF/UHF signals, etc.
If you don't want to buy an RTL-SDR, you can search KiwiSDR which is a streaming SDR for frequencies under 30MHz. You can also connect to KiwiSDR's worldwide.
Then if you get the itch, you can go get your a HackRF, a ham license, or whatever else scratches it.
Ham radio operators looking forward using them for 13cm and 5cm band stuff.