I think the idea of telling the story of Superman from the days of Krypton to the end of the present world is an idea that could work. But, it must be done so that the story ends with hope, not despair. That is the real message of Superman, after all, so here's how they could do it as a trilogy and still keep it faithful to the stories as told in D.C. Comics:
Part One being on Krypton:
Name of the Movie - Superman: World of Krypton
Use the post-crisis "World of Krypton" mini-series which was a re-imagining of a much older, pre-crisis series of the same name. I read the post-crisis one, and it was an awesome story that reveals the reason why Krypon blew up in a way that has never been explained on T.V. or in any of the movies. Here is what I remember about it; it was done very sci-fi and very, very epic:
Jor-El lives in an age of Krypton where love is considered secondary to the advancement of scientific knowledge. As a result, his love for his wife is seen as something unusual to the average, "practical" Kryptonian. One day, Jor-El decides to research his family history, but discovers that something long ago happened that the Kryptonian government doesn't want anyone to discover.
So, despite the danger, Jor-El keeps digging deeper and finds out that one of his ancestors was a war hero who fought against a terrorist organization that was called Black Zero in an age when Kryptonians were more passionate and less logical. In the very hour of their defeat, Black Zero lowered a huge bomb into a shaft that would eventually reach the core of the planet. The bomb would not reach it's target for centuries, since Krypton was so large. In the years following Black Zero's defeat, the Kryptonian government tried to keep the fact of the bomb quiet. Now that Jor-El knew about it, he tried to warn people but no one would believe him. To the Kryptonian government, it was more important to cover the truth than to let it be known. In secret, Jor-El builds an escape craft and decides to send his and his wife's child, Kal-El, to another planet (Earth) where he would be safe. Kal-El is sent to Earth on the very day the bomb finally reaches Krypton's core, destroying the planet.
Why this storyline is perfect for a new generation of Superman fans: it deals with all the issues we face today - terrorism, global catastrophe and whether or not it is true or false, and the importance of love in a technological society.
Part Two being on Earth in the Present:
Name of the Movie - Superman: Man of Steel
Take any post-crisis Superman where he grows up with the Kents alive and well, put Lex Luthor in the background as a shady businessman that the law can't touch, and introduce a new and more potent villain for Superman to go head to head with. Or better yet! Have Part Two be a montage of the whole of Superman's career. Him saving people from disasters, fighting the powerful villain, and gaining a reputation as a savior of humanity. This will be vital to his peril in the third movie, where he finally realizes his own super-mortality.
The villain: General Zod would be perfect, and here is why...
He could be explained as the last criminal remnant of Black Zero on Krypton. Jor-El captured him and the Kryptonian government had him exiled into the Phantom Zone. Thus, he escapes Krypton's destruction and finds his way to Earth where he encounters Superman. Both are equal in power due to the sun's effect on them and Zod could utter a taunt such as: "You can't save them forever, Kal-El! Someday, just as Krypton perished, this Earth will too."
That will be a foreshadowing of the final events covered by the third movie.
Supporting villain: Brainiac could fit this role, and here is how...
Brainiac could be envisioned as an alien with powerful mental abilities who witnessed the path Kal-El's spaceship took to earth. His people were old enemies of the Kryptonians so he hates the house of El. Therefore, when Zod breaks out of the Phantom Zone, Brainiac arrives on the scene (picking it up on his ship's scanners) and when Zod asks where Jor-El is, Brainiac could tell him of Krypton's demise, Kal-El's escape, and the route to take to get to the planet Earth. When Zod first attacks Metropolis, Brainiac assists him. Before he can defeat Zod, Superman will have to deal with Brainiac's own schemes.
The role of Lois Lane: Superman and Lois Lane's romance is tragic...
Superman will live forever, but Lois won't. But, Like Jor-El, Superman values love and decides it is worth the sacrifice that he will ultimately have to make.
Part Three being on Earth in the Future:
Name of the Movie - Superman: Darkest Hour
Here, we are in a "What If?" future scenario where Superman fights his final battles and eventually discovers that even an ending can be a new beginning.
The movie starts in the present, after the events of the second movie. Upon defeating General Zod, Superman gains a reputation as a man who can keep the Earth safe no matter what. The early part of this movie could cover the Doomsday story arc with Doomsday coming to Earth, killing Superman who is then revived, and Superman finally defeating Doomsday. At this point, Lois sees that either of them could lose the other, Superman not being nearly so immortal as is assumed. Flash forward into the future as we see Superman grieving for Lois Lane who died of old age while he himself is still young. The main villain comes in at this point: Darkseid, who like Superman, is immortal and will likely live even when the Earth is no more. There is almost a Christ vs. Antichrist conflict where Darkseid attempts to take over the Earth and people wonder if Superman will save them since he's been out of the picture for so long, mourning Lois Lane. He gets over her loss in time to fight against Darkseid and defeat him, restoring peoples' faith in him. Now flash forward to an even more distant future: Darkseid is still a threat to what remains of the human race, and Superman and him have been battling on... oblivious to the state the planet is in. The sun has begun to perish, and everyone Superman every knew or cared about is long gone. All he has left is the desire to fight against the evil, alien god who still threatens the Earth. This conflict mirrors Jor-El's ancestor fighting Black Zero: no matter the outcome, the planet is doomed. Finally, Superman forces Darkseid to retreat back to his homeworld of Apokalips, where Darkseid admits there is nothing left to fight over. "Will you stay on a dead world out of misplaced loyalty, Superman, or will you do like your father did and consider there may be other worlds in need of such a hero as you?" could be the final taunt as Superman loses his powers. Then, a final scene shows Superman at Lois's grave saying something like: "You were a good people. You just needed someone to show you the way." Echoing the words Jor-El spoke in the old Superman movies. The sun then goes dark and then bright as it explodes. In a brief flash we see Superman is no longer at Lois's grave. Then, the Earth explodes and Darkseid's words play out across a cosmic starscape: "Will you do like your father did and consider there may be other worlds in need of such a hero as you?" Then, the shot pans out to a distant galaxy with a sun not unlike our own. In fact, this other galaxy looks identical in every way to ours! A blue and red object is seen streaking at a high speed towards an Earth-like planet, but the object is not seen clearly.
On this Earth-like planet, the object is seen as a meteorite which lands on a farm where we see (although not clearly) a man and a woman who sound a lot like the Kents. They touch the metorite and it crumbles, revealing a baby boy wrapped in Superman's costume. They pick up the child, and say: "Oh, my! Wherever did you come from?" and then the credits would roll.
What would make this a legend, not just a movie:
This would reveal that Superman isn't dead after all, just powerless (reduced to a baby again) by the explosion of the sun. Now, under a new sun on an Earth that is a parallel Earth to our own... he'll grow up (with no memory of anything that happened before), and become the savior of that Earth too.
Thus, the cycle will be complete and the story will end just where it began.
Which Earth was really ours, therefore, and which one was the parallel Earth? That could be the final, unanswered question and leave Superman with an of ending designed to make people think deeply about the mythos in the same way people think of the Norse myths. They end with Ragnarok, but the gods return in a new world following the destruction of the old one. This would do for Superman what Frank Miller's The Dark Knight Returns did for Batman. Add closure to the story without killing the character. The Superman vs. Darkseid parts would let them show off the Angry God aspect of Superman that was discussed in early talks about this reboot. In this case, you'd have two angry gods literally fighting one last apocalyptic battle in true mythological fashion: one Christ-like, the other a demonic Satan-like figure who mixes truth with lies in true Miltonian tradition. Deep philosophical moments could have the hero wondering: "At what point is a cause lost?" With the ending showing that no cause is ever lost for good. This would take Superman as dark as you can go with him while still showing him as the unbeatable hero.
The reason why this ending would be true to the comics:
In the Superman comics, parallel earths have been an issue since Crisis on Infinite Earths and before. This way of ending the Superman trilogy would be in the spirit of those stories and very true to the style of D.C. comics.
I know they probably won't do anything nearly this mythical, but it would be the best way to tell this story while honoring the lasting legacy of Superman.