Scanner Radio Pro

Because somebody should watch the watchers.

This is a great app for listening to police, fire, and emergency radio transmissions. 

First a breif personal anecdote:
I've owned a couple handheld radio scanners in the past, and I actually been arrested for listening to one in my car once (it used to be legal to do that where I lived but they had changed the statute recently and I didn't know).  Charges were eventually dropped because I had a press pass for a major publication, and members of the press were exempt from the new statute banning their use in motor vehicles.  One nice thing about this app is that it doesn't actually monitor radio frequencies, it monitors transmissions from other people who have scanners set up to monitor the radio frequencies.  So it shouldn't be illegal in any way but you may want to check local laws to be sure.

This app has some pretty good features and capabilities, such as:
Listen to live audio from over 2,500 police and fire scanners, weather radios, and amateur radio repeaters from around the world (with more being added daily).
Configure alerts to have the app notify you when lots of people are listening to a scanner (indicating that something big may be happening).
A handy widget that lets you toggle the scanner on/off right from your home screen.

Cost: $2.99 for the full version, but there's a free version available with some ads and the widget is disabled.

Some screenshots(not taken by me, because I use an older version):

Well writing this gave me an excuse to update to the latest version(and i really like the new look), so I might as well skip the QR code and just say click here to get it.  That's assuming you have a rooted phone, and know what to do with the .apk file.  That's the full version too.  Umm if you want the free one or don't know what to do with that file, here's a QR code for you:

PROTIP: you can install the full version and the free one and listen to 2 scanner channels at once.