Warning: The following may contain spoilers (depending on how you define spoilers).
Braid's one of those things that everyone sees differently. Be warned that this is a stream of consciousness, that was written in patches, and so doesn't flow terribly well.
I suspect that the game shows several different people. There's the atomic bomb scientists element, the child, and the romantic relationship. There's always the idea that it shows one person at different stages of his life, of course.
The majority of the game seems to focus on the romantic relationship. The main plot is that of Tim searching for his Princess, and the introduction talks about a girl, and a relationship without mistakes - or, at least, where the mistakes can be learned from, and the experience kept, but the consequences lost. There's the ring. It's interesting, although probably not symbolic, that the further away Tim gets from his ring, the faster he runs. And, yet, if you leave it behind, it shows up right there in your pocket again, as if it never left. Time stops, around the ring.
Then there's the woman he talks about leaving. The one who loved him anyway, all the while he was gone, Princess or no. I suspect that that's the segue into the atomic bomb segment of the game. The scientist who searches, who makes us all sons of bitches.
There are a number of fragments which seem to be talking about the discovery of the atomic bomb, and some people have pointed towards the Princess exploding, if you manage to catch her.
Then there's the child, who wants to get into the candy store, and considers using violence against his mother in order to get what he wants.
Maybe it's one character, who transfers his desperate obsession to something else, every time he gets what he wants. Maybe, he did find the Princess, every level, every time, and then rewrote the story so she was always one more step beyond him. Maybe what Tim wants is to be searching.
I don't think the singular character or the specific narrative are important. To me, the game's about obsession. It's about searching, and trying to move forward. What Tim wants is less important than the fact that he wants it, desperately, and goes through fire and goombas to get it.
And yet, assuming he doesn't do it on purpose - or maybe because he does - Tim is destined to fail. He failed before he even began. And yet, he hopes. Maybe, if he goes back, and changes this, and changes that, and does this in a different way, he can find the Princess. Maybe, if he goes right back to the beginning, things will be different.
So there's another theme. Alongside the obsession, desperate hope that will never succeed.
There's also the longing for the past. The game's purposefully reminiscent of the
Mario games. If Tim is in his thirties, that would make him a pre-teen around the time those games began. Tim, whoever he represents, is living in the past, in more ways than one.
The images which accompany the five worlds (which can be seen
here), the jigsaws whose pieces Tim collects, show another story. They show a man with a woman, reaching for a wine bottle. At what seems to be a dinner party, offering a toast. Then, a child's room, a terrified child on the bed, and a blurred figure opening the door and looking in. A child - the same child? - on what seems to be a school trip, drinking from a can, alone. A man with dead eyes, looking at a ring in a pile of trash. Is he walking towards it, or walking away?
The pictures aren't necessarily in chronological order, of course. Maybe they show a story spanning two generations, Tim's father's problems leading to his own. Or, maybe each picture shows Tim, as he grows up. Maybe the final picture, the ring, is him walking away from his marriage. Or, maybe, from the way it glows, that picture marks the start of Tim's obsessions, when he sees something in the rubbish that no one else values, something that calls to him.
In summary, here's a recap. The story begins in World 1, with Tim finding the Princess, and her running away from him. She's alarmed at his presence - he's an intruder, and a threat.
The Princess is then carried away by a Knight, and Tim searches for her, through five more worlds. At the end of each world, he is greeted by a strange dinosaur creature. The first one apologises, and says the Princess must be in another castle. The final creature asks "are you sure she even exists?"
There's a very interesting thread discussing interpretations of the game
here.
