What's the safe limit on charger output for a Galaxy Nexus The charger that came with my Galaxy Nexus phone outputs 5 volts at 1 amp. I have another charger that outputs 5v at 2 amps. Is it safe to use this charger? What's the limit I can use without damaging the phone?
All phone (wall-type) chargers are voltage sources, i.e. the adapter provides a stable voltage output (5V here) and the device decides how much current to draw. Your charger's specification says it provides a maximum of 2Amps. That means it will sustain its 5V output voltage up to a current of 2A.

The phone's internal charging chip may or may not charge the battery in a voltage or current driven means (Li-Ion are typically charged voltage driven and current capped if I'm not mistaken). However this is completely hidden internally and you don't have to worry about it.

If the adapter can't handle your phones current need, it may get hot or the phone may just discharge (instead of charge).

It may even be the case that your device draws less than it would need to charge (if you do navigation for example): What causes battery to drain faster than it can charge?