To me, for a character to be over powered/broken he or she has to be extremely powerful while not having any weaknesses be it physical or mental (psychological or emotional)
I'd have to say that Superman is pretty over-powered/ broken. While I've never read Superman comic books I have seen a couple movies and the animated series and I've noticed that Superman really doesn't have any emotional, physical or psychological problems to deal with, other than maybe identity issues stemming from his home planet being destroyed.
Doctor Manhattan is super powered but ,in my opinion, that is balanced out by emotional and physical traumas from before and during his transformation such as his father demanding that he go into science rather than stay in clock repair, the physical pain from being torn apart at the molecular level and even his lover/girlfriend running away right be fore he 'died'. Then there's his continually growing detachment from mankind.
Wolverine's power's are somewhat balanced by his own problems, memory-loss feeling the pain of every injury he receives and the loneliness of outliving so many people he cared about.
Ed from Fullmetal Alchemist, who was mentioned before, spent years training to become an Alchemist, and over those years has gone through s shit load of emotional, psychological and physical trauma. He has abandonment and anger issues concerning his father, has lost an arm and a leg due to a botched human alchemy attempt, has witnessed first hand murders and deaths, several of which he was responsible for (either directly or indirectly)
Even the Punisher, who has survived numerous beatings, stabbings and shootings, has severe emotional and psychological problems
