Fading-out is a way to end a song that has no obvious ending. Usually the chorus or a phrase is repeated endlessly as the volume slowly decreases. Ending songs with a fade-out never bothered me but I've talked to people that find it a "lazy" bad habit in song writing.
At one time I would say that almost every popular song in the USA used fading at the end. It was so commonplace that when a piece of music actually had a hard ending, that song really stood out when heard over the radio.
I heard somewhere that radio DJ's used a song's fade-out as a shortcut to edit a song just before a commercial break. Let's say you had 2:59 min. available airtime and a record running 3:00 min. The DJ could talk over the fade-out and go directly to break.
For broadcast purposes, fading is just fine. But wow - try your luck in a live concert. Imagine bands that had fading on all of their hit tunes. Many bands try creating endings so that live performances are not so awkward.
I think "Rolling Stone" asked readers for their favorite fade-out tunes. One song on most people's list is "Hey Jude", the Beatles ran that fade-out a real long time. The boys over at "Sound Opinions" in Chicago picked 10CC's hit, "I'm Not In Love" as their example of the greatest fade-out of the 70's.