For me a great hi-fi doesn't necessarily have to be the best-sounding one.
It's more about a sound that draws me in. One CD or LP leads to the next, and I don't want to stop to eat, read, go to bed, or watch TV. A great hi-fi is one that lets the music cut loose. Even cheap gear might have what it takes to get my juices flowing. Take the Velodyne vPulse in-ear headphones; they make too much bass and are far from the most refined headphones in my collection, but I keep using them. I don't need to, the review has posted, but there's something about these little headphones that keeps me coming back for more.
I have fond memories of the first hi-fi I bought with my own money--it had a Garrard turntable, XAM speakers and amplifier--and the sound of my Jimi Hendrix and Doors records was beyond amazing. I never got over that sound, or felt as energized as I did when I was 16 and played my music over that little stereo.
I hope there are a million 16-year-old kids out there listening to headphones right now, experiencing the same sorts of thrills I did. Or maybe it's happening in a car, and they just heard a tune they'll remember forever. For some it might be a home theater that brought movies to life.
As for the best-sounding hi-fi, I have fond memories of playing Wilson Audio Watt/Puppy speakers when I worked in a high-end audio store in NYC in the early 1990s. That system sounded best when played nice and loud, so rock music had the visceral kick of the real thing. The Watts weren't perfect, they didn't click with classical music, but they were always exciting to listen to.
Please share your audio awakenings here in the comments section.