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I might sound foolish but I will risk it. I think the most fascinating trait of Raskolnikov is the combination of his good looks, self-confidence and his intelligence. Remember that the book begins with him being described as a rough good looking man. You might think that's shallow but that's usually one of the tricks into making certain complicated characters more likable. Second to his good looks is his self-confidence. Danne might call it arrogance but let's face it, wearing the cape of confidence has made many awkward moments flawless and in some situations---right many wrongs. Last but not the least would be his intelligence. Had he been a dumbass I'm sure I wouldn't even bother understanding him. We always give second chances to smart people especially if they show signs of having a heart. :P

If he weren't good looking, confident and smart---you'd have a helpless conflicted guy. Hell, he might not have killed the old woman had he not believe himself to be so great. I'm not choosing one trait from the three, because those three traits wouldn't work without each other.

I am fascinated by Raskolnikov's almost schizophrenic internal struggle between his arrogant self-justification and guilt. This is what drives the whole plot right up to the end of the book.

Psycological strain.. btw, a recuring theme of Dostoevsky. Just like Kubrick.

I think, the most bold (may not fascinating) trait of Raskolnikov which is the reason of his psychological strain (the term used by @Bruno in his comment) is his Idealist personality. He was desperate and hopeless because of his terrible (financially and emotionally) situation. In this situation, an idealist (as Dostoyevsky himself was) may think and ask himself about his identity and suffers from the bad feeling of his failure to reach his ideal goals. He knows that he failed in his plans and dreams. That's why it seems that he is a mere nothing. I think it's the immediately consequence for an idealist, who thinks that he can be a hero but the social and financial obstacles prevent him to be what he deserved, that every social rules and regulations becomes meaningless for him. He may break those rules for protestation to show others that I AM or for revenge the society by violating their rules. However, because of his kind and sensitive soul (remember his childhood memory about seeing a violent scene and his reaction), he could not tolerate his opposing action against society.

On the other hand, Raskolnikov (unconsciously) wonders whether anyone (e.g. his mother) loves him after committing the crime (breaking those rules) or not. In this action, Roskolnikov may seek his identity in love. I mean, he exists because he can be loved by the others.

In addition, it's interesting for me that there is a common personality aspects in Raskolnikov and Meursault (in The Stranger by Albert Camus): "Indifference" to the what's going on in the reality and "emotionally detachment" to their environment.

By the way, It's really interesting to see these psychological facts in a novel written before the emergence of psychoanalysis (Dec. 1899). I love Dostoyevski! :D

P.S - I'm writing in English which is not my native language. I tried to say as close to my thoughts as possible! :)

doesn't Raskalnikov translate as Schism? as in fracture?

i remember a russian mate telling me this was the case.

Schizophrenia is one of D.s favorite subjects. Many of his characters possess the malady.

Najviše me je impresioniralo kod Raskoljnikova ta njegova odluka da izvrši ubistvo dvije babe, a da se uopšte ne razmišlja, a onda ga to počinje mučiti, jesti danima, ubijati. Znojio se, padao u teška psihička stanja.. Najzanimljiviji dio mi je onaj kada mu inspektor objašnjava kako on svoje kriminalce pušta na slobodu, daje im slobodu kretanja, ali iz razloga da bi ih mučio, da bi patili, i na kraju, kada ne bi više mogli, došli i prijavili se sami.
Tim riječima je i Fjodor htio dati pouku čitaocu za slobodu kretanja Raskoljnikova, sa veoma dobrog i temeljnog psihološkog aspekta..

arrogance...
simply because, why would you think that you're a napoleon if you isolate yourself to others?
he just don't want to meet other people because he thinks that he is on a different level even though he haven't prove anything yet.
raskolnikov is like bobby fischer, the 11th world chess champion, they think that everyone around them is inferior to them. Their difference is that fischer is a genius and raskolnikov is a mere nothing.