Obvious picks for this activity are the chapters "Rebellion," "The Grand Inquisitor," and "Ivan's Nightmare and the Devil." I'm also fond of going over the story of Ilyusha and the boys every once and again, and I recently gained a renewed appreciation for the chapter with Lise called "The Hell Kitten" (also translated as "The Little Devil," I believe).
I'm sure that I'm neglecting some of the very best parts in the book, and the reason might be that I wasn't paying enough attention to them while I was reading this book the first time around. So I ask you, Dostoevsky community, if anyone else out there has some favourite chapters that stand out and that you enjoy reading, or that you feel are generally underappreciated and worthy of closer examination? I love the activity of re-reading individual chapters in this book but it's pretty hard (for me, at least) to remember where the best stuff is at.