With an Android app called Scanner Radio, you can turn your Android phone into a portable police scanner. Volunteers with scanners provide over 3,100 audio streams from police and fire departments, weather radios, and amateur radio operators.
You can let Scanner Radio search for scanners near your current location, or manually search for scanners based on area, genre, or source.
Once you find your favorite audio feeds, you can add them as favorites for quick access. You can also listen to archives of certain feeds, but that feature requires the Pro version ($2.99).
That's it. Just a little warning: listening in on police scanners can be addictive and scary, all at the same time.