Cobb the Explorer
It's pretty clear right from the get-go what kind of guy Cobb is. He and Arthur are in Saito's dream, and Cobb, despite knowing they've been compromised, still risks breaking into the safe, stealing information right in front of Saito, saving (well, killing, but it's kind of the same in a dream) his partner from pain, and outrunning and gunning a bunch of projections and reading the document...while the entire dream is collapsing around him.
Cobb gets things done no matter what stands in his way.
An army of projections seeking to destroy him and his team? No worries. A vindictive projection of his dead wife? Not a problem. (Okay, she's kind of a problem, but we'll get to her in a minute.)
Cobb is also a man of exploration. Like Ariadne, Cobb was once an architect studying under Miles. However, he became obsessed with the dream world and wanted to explore all of its possibilities. In fact, the reason he and Mal became stuck in Limbo was because of his desire to go farther, to go deeper.
Just as he's willing to explore every nook and cranny of the dreamscape, though, he's also willing to do whatever it takes to return to his family, even if that means purposefully going back into Limbo to confront Mal… and risk losing his own sense of reality.
Guilt on the Cobb
When Saito asks Cobb if he wants to end up an "old man filled with regret," it strikes a chord in Cobb. Cobb is already regretful because of what happened to Mal. It was Cobb who pushed further and further into dream space, so he feels responsible for her eventual suicide.
He's a haunted dude.
Cobb's guilt isn't just about what happened when he pushed the boundaries of dream sharing too far; his guilt comes from what he did to remedy the situation. Cobb is responsible for planting the doubt in Mal's mind that her world (the real world) wasn't real.
In their final encounter, projection Mal asks Cobb, "What do you believe in? What do you feel?" to which he replies,
COBB: I feel guilt, Mal.
This guilt is greater than we could have guessed. Not only does it define Cobb, but it also brings up a question in our own minds as to how responsible Cobb actually is for Mal's suicide.
How much guilt does he deserve to feel?
Cobb is even still more complicated when we take into account that any characterization of Mal as a projection is actually a characterization of Cobb himself, his understanding of Mal, and his subconscious. Basically, every time you see Mal—flashbacks excepted—you're seeing a facet of our man Cobb.
Cal and Mobb may not make great couple nicknames (they're pretty horrific) but the real Cobb and projection Mal make quite the combo of Cobb's conscious and subconscious selves. While Cobb consciously feels very guilty for his wife's death and is desperate to see his kids, his subconscious is stuck on the idea of being with his wife.
In fact, Cobb is aware that, if he wanted to, he could make himself forget his wife is a projection and could spend an eternity with her in Limbo none the wiser. Remember that every single thing projection Mal says is Cobb saying it back to himself. Sometimes he's recreating a memory of her and other times he's expressing something that is unique to himself.
Ugh. There's a reason that this movie is such a brain-twister.
In their final encounter, Mal questions what Cobb considers to be reality, saying that it sounds odd that he is chased around the world by nameless corporations; it's almost as if in a dream. This is a scary thought but it's even scarier when we realize it isn't coming from Mal. It's coming from Cobb himself: he's doubting his own reality.
Now we know why he's so obsessed with spinning that top. Cobb is a man who has somewhat literally been torn in two—Mal and Cobb, subconscious and conscious—by his guilt.