This discussion is concerned with the standard credit-card size Raspberry Pi, not the embedded SIMM format embedded Pi.
The Raspberry Pi Foundation has power recommendations for each model of the Raspberry Pi. From the Rpi B+ onward, the Pi has an APX803 chip that monitors power state and flashes an LED under abnormal conditions. This same Pi power alarm LED can be controlled with software since it’s on GPIO.
Practical measurements and my personal experience indicate that B+ and later Raspberry Pis are stable with non-garbage power supplies. The problems I had with the old, original Raspberry Pi Model B scrambling the SD card repeatedly on a cheap old power supply weren’t experienced on the newer Raspberry Pi.