In the final scenes of Hannibal, Hannibal Lecter could have killed Clarice but he let her go and cut off his own arm, and there's also the perfume in the letter scene. So what exactly was it? Was it love, respect or what? What exactly made Clarice so important?
"Mischa, we take comfort in knowing there is no God. That you are not enslaved in Heaven, made to kiss God's ass forever. What you have is better than Paradise. You have blessed oblivion. I miss you every day." -Hannibal Rising
And so I came to believe, " Dr. Lecter was saying, "that there had to be a place in the world for Mischa, a prime place vacated for her, and I came to think, Clarice, that the best place in the world was yours." -Hannibal pg 535
Hannibal's obsession with Clarice starling derives from parallels he draws from both himself and with his dead little sister, Misha, whom died tragically, and whose murder he witnessed, is responsible for the origins of Hannibal's cannibalism.
In the novel Hannibal (as this part of the story is omitted from the film version) Hannibal, whose been playing some sort of cat and mouse game with Clarice for seven years, unexplainably gets it into his head that Clarice is the perfect vessel for Misha's conscious. However, Hannibal admits to both not being able to control Clarice, but also simultaneously tries to take credit for the manipulation by siting he built better than he knew, where Clarice tells him what better place for Mischa than in his own mind. Uncharacteristically Hannibal mostly accepts this and Harris is careful to word the final lines in the novel to suggest the characters have changed due to being in love. Hannibal sees less and less of Mischa in his dreams, and Clarice does not want to be "awakened" from her conditioning...
I wrote a great deal about this in terms of the TV series approach to the source material here: http://www.spoilertv.com/2014/05/hannibal-bryan-fullers-metamorphisis.html