Superman is a character who has been around for decades, and been through many incarnations. He has gained and lost powers, died and been reborn, even had some costume alterations. Many see him as over-powered and thus not interesting. I would argue that he is one of the most interesting heroes when portrayed correctly. Unfortunately this has been rare.
Superman is the alien among us. He looks like us but is not one of us, forever separate. He has godlike powers that he could use to enslave us all, but instead uses those powers to help and protect us. He is honest and virtuous and good natured, even though the weight of the world often rests on his shoulders. He is the epitome of what most people strive to be.
In efforts to make him more popular he has had alternate versions introduced where he is evil, or authoritarian, or angsty. However I don't think you need to change his personality or behavior to make him more interesting. You just need to realize what a wonderful array of things you already have to play with. My evidence for this assertion is the Cartoon Network series Justice League Unlimited.
It is my assertion this show is the best portrayal of Superman ever done. He has all the characteristics of the all powerful alien and also the midwestern small town boy who never quite grew up. It's the little details that hint at the larger issues that I love though. One example is how people address him based upon how they relate to him. Wonder Woman and Martian Manhunter, being a mythological demi-goddeess and an alien respectively, call him Kal-El, his Kryptonian name. Batman, being a "mere" human, calls him Clark, his earth name. The Flash Calles him Supes, not being close enough to call him by either of his given names.
When Superman faced off against Darkseid there was possibly the best moment the character has ever had. After taking a beating at the villain's hands, Superman comes to a realization. He talks about having to always be careful to pull his punches, because it would be so easy to unintentionally hurt or kill someone. Then he looks at Darkseid and says "But you can take it, can't you big guy". With that he unleashes, hitting Darkseid with a punch which shatters windows for blocks with the shockwave. This might be the only time a cartoon has had me jump off my couch and yelling encouragement at my t.v.
The point is, there is no need to make Superman dark or grim. Part of his appeal is that with the burdens he bears he does not give in to darkness. Man of Steel pointed out that the S shield is a symbol of hope. Here's hoping the film makers remember that soon.