The theme that prevails in all of his films, that connects all of them, is identity and identity conflict. It is the major focus of my book on Nolan that is near completion. Obsession and revenge are certainly there, but identity rules the roost. All of the major characters in his films have to grapple with some identity conflict to some degree or another. Allow me to quickly skim the surface and break it down:
Following: The main character is a writer that is bored with his meager existence. So what does he do? He follows people around to learn something about them, keep himself occupied. He becomes fixated on one guy in particular and then begins to emulate him. To change what he does and how he lives his life. He sheds his old identity to begin life as someone else.
Memento: This is hard to miss. The main character can barely remember what happens around him and who he is. He tries desperately to reconstruct the events of his life not only to unmask his wife's killer but to learn more about himself.
Insomnia: Not only is the main character trying to hunt down the identity of a killer but he is also trying to reconcile what he has done in the past with his present and future. He is haunted by an event from his past where he crosses the line of cop and criminal, thus becoming what he fights against. Throw in to the mix his struggle to sleep and you have someone who is slipping and trying to cling to the person he thinks he is.
Batman Begins: Bruce Wayne struggles with his identity as the richest man in Gotham. But he wants to be someone else. To tame this urge (or harness it) he becomes a masked crime fighter. He lives two lives and tries to mesh the two of them together. The film also delves into the nature of masked villains, like Scarecrow, who's true nature is not so well hidden from the public.
The Prestige: This one really discusses the nature of dual identities. The film is all about magic but also the nature of the identities that these performers assume and how it effects their lives, on and off the stage. Borden strives to achieve the perfect trick by using his identity and that of
to help him on all consuming quest.
The Dark Knight: In TDK we see Wayne really struggling to juggle both of his identities. We also get Harvey Dent, a man that is secure in his identity but also harbors a darker side that is waiting to be unleashed. His struggle with both of these identities is pushed to the edge with one winning over the other. The Joker is also the very absence of identity conflict, the complete reverse. He exists to cause chaos and destruction as a pure individual, and thus we don't get any conflicts or backstory. He just is.
Like I stated before, this really only skims the surface. There is so much more.