I would have to say Sango, I'm a sucker for character depth. Her story had me transfixed from the start, especially when a love story sneaks its way in! And I HATE it when Kohaku's in an episode because I'll bawling from the first note of the beautiful musical score that surrounds Sango! She even has a relationship with Hiraikotsu, and has showed true vulnerability in the face of trials, such as Naraku's ultimatum with Rin in the Final Act. Kikyo's got a lot of depth too but I sympathize with Sango more. And Kagura has lesser depth than Kikyo, but is more enticing.
Koga and Rin are my favorite static characters, for they are both token optimists and influence the story and other character's depths.
And, of course, Inuyasha and Kagome are my two favorite personalities, for they're what hooked me onto the show in the first place!(I anime'd before I manga'd! Oops!)