All three main characters in Candorville do this from time to time—Susan and Lemont because their problems are so great, Clyde because he's just self-centered. None of them have anything on Roxanne, though—she has never shown concern for any individual human being other than herself and her son with Lemont, and the latter is more a means of guilt-tripping Lemont than someone she really cares about.
Calvin, taking it to extreme levels in his six-year-old naivete. It comes up all the time, but perhaps the clearest example was when he used advanced cardboard box technology to create multiple identical copies of himself and was amazed and outraged when instead of doing all his work for him they all did whatever they damn well pleased and got him into trouble repeatedly. He has also remarked that the world owes him everything for the simple fact that he made it a better place by being born; that he's tired of everyone being so selfish and only thinking about themselves when they should focus on him; and that he's figured out his purpose in life, and it's that everyone do as he tells them to.
What may set some kind of a record is when two time-travelling versions of Calvin decide to gang up on the Calvin between themselves in time, blaming him for being lazy and not doing the homework assignment neither of them is going to do either because they want to get it by time travel. They threaten to beat him up to make him do it until he points out they're going to suffer from it too because they're him. In other words, it's not even just all about me at the expense of everyone else, it's all about me at this moment at the expense of me at other times.
Lucy van Pelt, who like Calvin has the excuse that she's a child. She's nothing but cruel to the other kids, yet expect them to treat her like a queen at all times. If she does something wrong, than it's Never My Fault. If there's a grievance against her, either real or perceived and usually perceived, she responds with a Megaton Punch. Most people, no matter how self-centered, would deny that they think the world revolves around them, but when Lucy is told in so many words that it does not, she is shocked at such an absurd suggestion.
At one point, studying history, Sally Brown is astonished to learn how many people existed before she was born. She feels sorry for them, because it can't have been much fun without her in the world. When Charlie Brown comes back from being lost in the woods, her reaction is "I suppose you'll want your room back?"
Snoopy is often prone to this.
The title character of Big Nate is OBSESSED with himself.
J.J. of Doonesbury - to the point where she somehow made the funeral of Widow Doonesbury (Mike's mother and her former mother-in-law) all about her forgiving Mrs. Doonesbury for the mean things she said about her over the years. For bonus points, she says this in front of Alex, her daughter (and Mrs. Doonesbury's granddaughter).
Bucky from Get Fuzzy. It's even lampshaded in one strip.