If you want to hear ambient noises—rain, thunder, wind, water, fire, forests, traffic, trains, arcades, planes, you know—check out Ambiphone, the latest single-serving site dedicated to this oddly recurring purpose. You can layer ambiences, and add "binaural beats" with theta waves and brown noise and what-have-you.
It's the creation of Matt Eason, a designer and developer: "I'm very grateful to the following people who created the sounds and music used in ambiphone. Their work has been edited slightly in order to loop it seamlessly."
You can also try a "find a sound" search box. I didn't get anything for "distant screams" or "sporadic gunfire", sadly, but there are deliciously anxious "police scanner" and "numbers station" buttons.
