A tip of the hat to my buddy JP who helped me on the research to put this list together!
In no particular order...
Saga of the Silver Banshee
Action Comics #595, Superman #17 and #23.
I loved this fresh new villain and its ties to Celtic myth and magic.
"Whatever Happened to the Man of Tomorrow?"
Alan Moore's fitting tribute to an amazing character. I've never saw Swan art
better than when it was inked by Perez.
Crisis on Infinite Earths #1-12
While technically not a Superman story, but Crisis had a deep impact
on the Superman Universe and it indeed would never be the same.
The death of Supergirl was beautifully pulled off as was
the graceful exit of Earth-2 Superman.
Superman in Exile (1989)
The first big storyline/crossover after John Byrne left Superman and
Roger Stern and company pull off a great story.
John Byrne's "The Man of Steel"
While some readers didn't like Byrne's reboot of Superman, it blew me away.
I always had a difficult time getting into the Curt Swan Superman, especially
in the early 1980s, so Byrne's reboot was a great way for me to catch up
on Superman and Byrne's efforts paid off, keeping me interested in the Superman
books for years afterwords.