I've only heard of the quote and have yet to read Dracula, but I was wondering what "Despair has its own calms" means?
"I passed to my room and went to bed, and, strange to say, slept without dreaming. Despair has its own calms."
It helps to see Harker's comment in context. At this point in the story he is growing increasingly frightened and disturbed by the behavior of the Count - each day he despairs more and more as he discovers the depths of his loss of liberty and the threat to his own life.
After a particularly chilling conversation with the Count he retires and sleeps, much to his surprise. The comment is a (short) way of saying, "The human mind has a way of finding some peace, no matter how bad things may be."