How much does volume matter when breaking in amps and cables?

tcatch, You may want to check your manual before running your amp without it being connected to speakers. Some amps will be damaged by that. 

Zero
What level on the sound system do you chose when you are "breaking in" your new car ?

I don't think the amount of volume is going to make any significant amount of difference.  I have burned in many cables, including speaker, at just low to moderate volumes.  Consider this.  Digital type cables (including spdif and hdmi) will typically only push 0.5 to 0.6 volts on the data conductors.  However, analog audio can be up to 1.4 to 2 volts.  In either case, both cables can be burned in with similar timelines.  Speaker cables will see significantly higher amounts of voltage (such as 5-50 volts or more, depending).  I think it's more important to send an amount of charge/discharge activity down the wire to help break it in.

I enjoy few things more than listening to a component as it burns in. The changes are just fascinating, especially the first few minutes to hours. Speakers, amps, cables, even fuses. Just one of the most amazing things, and I listen closely every time. In 20+ years I have heard no evidence volume matters at all.