As you've probably heard by now, Dostoevsky wrote Notes from the Underground in part as a response to Nikolai Chernyshevsky's novel What Is to Be Done?. Of course, Nikolai wrote his novel in response to Ivan Turgenev's Fathers and Sons, which is also referenced in… Notes from the Underground. Oh, and Vladimir Lenin was so inspired by Chernyshevsky that he wrote a political pamphlet called What Is to Be Done?
Dostoevsky's tombstone reads: "Verily, Verily, I say unto you, Except a corn of wheat fall into the ground and die, it abideth alone: but if it die, it bringeth forth much fruit." This is a biblical passage from the Gospel of John as well as the epigraph of his final novel, The Brothers Karamazov.
Dostoevsky has a streak of poverty in his later life (due to a gambling addiction) and wrote some of his most famous work as quickly as possible simply for the paycheck. Example? Crime and Punishment.