How extensive was the executions of prisoners and pilfering/plundering by US troops in Europe during WW2?

I'm watching the series "Band of Brothers" that portraits the course of an airborne company through Europe during WW2. In it pilfering of corpses, plundering of houses and the executions of Germans after they surrender or even after they were taken as POW are presented as routine with no one even raising an eyebrow.

Was that really the case? I'm sure such offences would've taken place (it's a war) how seriously were they dealt with by higher ups?