This is an interesting question. Usually you probably wouldn't hear if you were just slightly running out of power. I had an interesting experience with a new McIntosh amp.
A little over a year ago I bought a new McIntosh MC152 amp (rated at 150 wpc), with a speaker protection circuit called Power Guard. Here's a brief explanation. "a proprietary, patented signal overload technology designed to prevent amplifiers from clipping and over driving, which protects your speakers from potential damage. It continuously monitors both the input and output audio signals, making micro-adjustments in real-time to preserve sound quality".
My room is fairly large, and I have MoFi Sourcepoint 888 speakers with an average of 6 ohm impedance. During a listening session I was listening to AC DC Thunderstruck. It was sounding so good, I kept slightly turning it up. At one point I noticed the Power Guard LED's were slightly flashing. This told me I was starting to run out of clean power. It still sounded great, no distortion to my ears, but this sort of bothered me. I would feel better with a little more headroom. Well, I traded it in for a MC312 (300 wpc with a 2.7dB headroom). Problem solved. I think better to have too much and not worry about it.