Galaxy Nexus randomly shut downs while streaming music with Pandora- how do I fix this?
For random shut downs, that's most probably a loose battery problem.

Stick some dental floss (I used Oral-B Glide floss) in the side opposite the battery connectors.  I used that floss because it's a bit spongy when you bunch it up but at the same time hard.  Used about 1.5 feet of it bundled up in my Nexus S phone.



When you push the battery in, make sure it is tight, but not too tight.

This will force the battery to remain contacted at the pins.  When the battery is loose and can disconnect from the pins (for even a fraction of a second), you get an open circuit and the phone shuts off completely (no power).