I watched this movie Saturday on TCM and was shocked to see Shatner as Alexey. Didn't recognize him at first in his monk haircut. An understated performance -- not a lot of Kirk-isms. A solid debut.
I was aware of the novel but successfully avoided Russian fiction as an undergrad. When I saw it playing I tried it to get an introduction to the story.
Overall, I enjoyed it. The plot centers on the manipulations of the Karamazov patriarch, Fyodor (Lee J Cobb), who has control of an inheritance. This leads to infighting between the stepbrothers, troubled romances, and murder. It touched on the religious and moral themes which are more deeply explored in Dostoevsky's novel (I hear). Apparently the ending differed from the book to make it a bit more uplifting.
Brynner and Basehart were both very good. Apparently Marilyn Monroe was desperate to play Grushenka. That would've been... interesting.