In “The Incident,” a story written by David S. Goyer in Action Comics #900, Superman creates an international incident by non-violently supporting the actions of Iranian protestors in Tehran.  When his actions are criticized by a National Security advisor, the Man of Steel replies: “I’m tired of having my actions construed as instruments of U.S. policy.  ‘Truth, justice and the American Way’—it’s not enough anymore.”  He goes on to say that he will renounce his American citizenship at the United Nations the next day.
Of course this is not a done deal.  The Krypton-born illegal alien hasn’t actually pulled the plug on his American citizenship yet and such an action would be a major gamble for DC Comics.  It’s in the U.S. after all that the vast majority of Superman comics are sold, and comic fans are a notably conservative lot when it comes to major changes in the nature of their iconic heroes.  "Going global" could be a feckless strategy indeed, if this storyline proves to be a major change of direction for the character rather than a provocative tease.
Yes it is true that renouncing his American citizenship would not necessarily mean abandoning his principles, just shedding a national identity.  Certainly the world has, as the Man of Steel points out, become smaller and more connected, but with a major Superman movie in production, this would appear to be a very bad time to forge a major change in Superman’s identity.  Will Superman follow Captain America, who became disillusioned with Nixon’s America and became Nomad in the 1970s?  Even if Supes does embark on such a perilous course, like Cap, his status as a “citizen of the world” is likely to be short-lived.