Superman and the Men of Steel (Action comics vol 2 #1-8) Is the latest origin of Superman and the perfect place to start in the New 52. The story has elements of the golden age Superman and shows the first days of Clark Kent as his alter ego. Still not at his full potential Clark has to fight the army, an alien menace and the organized crime in metropolis. By Grant Morrison and Rags Morales.
Superman: Birthright Is a retelling of the origin story, a maxi-series that seeks to modernize the character while installing new elements.A fan-favorite comic book by Mark Waid and Leinil Francis Yu.
Superman: Earth One Is part of the E1 series that allows the writers to explore the characters from a different angle. This title is more than a simple origin,the writer explores and defines the place of Clark Kent in the world. By J. Michael Straczynski and Shane Davis.
Superman: For All Seasons Is a story of the early years of Clark Kent as Superman. Seen from the eyes of those closest to him on both sides of his life good or bad! By Jeph Loeb and Tim Sale.
Superman: Red Son Have you ever thought how would superman turned up if he was raised in Stalin's Soviet Union! This title is part of the elseworlds imprint and answer's the previous question. It mixes alternate versions of DC super-heroes with alternate-reality versions of real political figures such as Joseph Stalin and John F. Kennedy. By Mark Millar and Dave johnson.
Superman: Secret Identity A very unusual story.A boy named Clark Kent who lives in a world where superheroes exist only in comics(simillary to ours) gains superman's super powers and his world changes upside down, the art is fantastic and the story really wins the reader.ByKurt Busiek and Stuart Immonen.
Superman: Secret Origin Is the last retelling of the origin of superman before the New 52 relaunch. The writer draws inspiration from the silver age of comics. By Geoff Johns and Gary Frank.
All-Star Superman is a beautifully written tribute to the Superman of the silver age. It's a refreshingly modern take on the character told with imagination and creativity.Usually considered the best Superman story, by Grant Morrison and Frank Quitely.
Kingdom Come Although not completely a Superman story,Kingdom Come defined the character in the 90s. Set in a future where the heroes of the old times have retired and the ones who took over lacked every moral and responsibility. It is when a major disaster happens that Superman decides to rein in the new generation of heroes in the hopes that they would reform and adopt his generation's ideals of what being a superhero is all about. Kingdom Come is the ray of light in the dark and moody comics of the 90s. By Mark Waid and Alex Ross.
Superman And The Legion of Superheroes Superman teams-up with his childhood friends from the future to stop a war that has been raging on the entire galaxy.The story talks racism and divide's the alien and human part of Superman.By Geoff Johns and Gary Frank.
Superman: Brainiac The breath-taking arc that took place in Action Comics #866-870. The first encounter between Superman and the real Brainiac is packed with a lot of action and changes in the life of Clark Kent. By Geoff Johns and Gary Frank.
Superman "For The Man Who Has Everything" this is a brilliant one-shot Annual from the mid-80s. It tells the story of Batman, Robin and Wonder Woman visiting Kal-El in the Fortress for his birthday only to find that an apparent "gift" (actually from the tyrant Mongul) of a parasitic flower has burrowed into his brain, shutting him off into a fantasy world of pure happiness. By Alan Moore and Dave Gibbons.
Superman "Up, Up and Away", Over a year has past since Clark Kent lost his powers, now Clark lives a normal life having left the Superman persona behind him. Still fighting for the weak Clark attacks Intergang through his articles. But when Intergang fights back and Lex Luthor returns, the world will need a Superman. The story is part of the ONE YEAR LATER event. By Geoff Johns, Kurt Busiek and Pete Woods.
Superman "Whatever Happened to the Man of Tomorrow?", Imagine that, somehow, the adventures of Superman were drawing to a close, never to begin again. This is that final tale: one of the most dramatic Superman stories ever, in which the Man of Steel makes his last stand. Huge cast of heroes and villians. This story marked the end of the bronze age of comics. By Allan Moore and Curt Swan.
Superman "What's So Funny About Truth, Justice & the American Way?" , " Dreams save us. Dreams lift us up and transform us. And on my soul, I swear... until my dream of a world where dignity, honor and justice becomes the reality we all share -- I'll never stop fighting." From only that line you can understand the awesomeness of that story. A new team of superheroes emerges ready to take lethal actions. As the popularity of the team increases, Superman wonders if the world has outdated him. By Joe Kelly,Doug Mahnke and Lee Bermejo.
The Death Of Superman : Nothing was the same after that story. Doomsday a monster of unknown origin rises from the depths of earth destroying everything in his path. The Killing machine must be stopped and only Superman has a chance against the monster. The biggest match in the history of comics which led to the death of the Superhero legend. By a huge cast of writers and artists that i don't remember now.
Superman: Camelot Falls It's "Must There Be a Superman" written large! The general concept deals with Superman and other alien super heroes having an effect on the earth's recurring cycles of peaking and destruction of society (such as rome, camelot etc...hence the name 'camelot falls'). By Kurt Busiek, Carlos Pacheco and Jesus Merino.
Superman in the 50s Is a collection of the most memorable superman stories of the Golden Age. By various writers and artists.
Hitman "Of Thee I Sing" Superman fails on his mission! Feeling guilty for not being able to save a astronaut, Superman has a by heart dialogue with Tommy Monaghan. By Garth Ennis and John McCrea.
Superman Kryptonite Nevermore Originally published in 1971, this story turned Superman's status quo on its head by featuring a story in which all Kryptonite was destroyed! But that leaves The Man of Steel anything but invulnerable as his powers slowly begin to fade and a doppleganger Superman arrives on the scene with strange powers of its own.By Curt Swan,Dennis O'Neil and Murphy Anderson.
Superman: For Tomorrow.One of the best illustrated Superman stories! Superman was out of earth for some time and when he comes back he finds out that people had dissapeared all over the world, one of them Lois Lane! For Tommorow has a bit darker tone to it and some may not find Superman as his usual self but the story delivers great dialogues and the plot is really well thought! By Brian Azzarello and Jim Lee!
Superman: Godfall Metropolis still tries to recover from a series of catastrophic events and their symbol of hope Superman is missing! Not even his wife Lois Lane knows where he is. Back on Krypton, Kal-El has forgotten everything about his past on earth. As he slowly regains his powers Kal-El is brought to the middle of a horrific conspiracy. By Joe Kelly,Talent Caldwell and by the late Michael Turner.
"Must there Be A Superman" A good, classic story that examines the continuing question of what Superman's place is in the world, and whether he does more harm than good. This is the story that first brought this popular aspect of Superman! Does Superman hold back humanity by saving them all the time!?By the mighty pen of Curt Swan and Elliot S! Maggin.
Superman: Emperor Joker What happens to the world when Joker gains absolute power? Superman becames a villian and have to solve why the world has gone insane! By Jeph Loeb, Joe Kelly and Ed McGuinness.
Superman/Batman: Public Enemies A kryptonite asteroid is headed for earth! President Lex Luthor declares Superman and Batman enemies of the state putting a 1 billion $ bounty on their heads. By Jeph Loeb and Ed McGuinness.
Superman/Batman: Supergirl The second arc of the Superman/Batman series. the kryptonite asteroid is revealed to hold a pod that contains Superman's cousin Kara Zor-El. The arrival of Kara catches the attention of the amazons, Apokolips and the attention of the whole superhero community. By Jeph Loeb and Michael Turner.
For more stories you can look at ComicVine's Top 100 Superman Universe Stories.