I had immersed myself in the Russian poets who were Brodsky's precursors (Akhmatova, Mandelstam, Pasternak, Tsvetaeva, Blok), then started reading him, since Akhmatova referred to him at the end of her life. (Brodsky's attendance at Akhmatova's funeral was one of the reasons the Soviet authorities went after him.) At the beginning I found Brodsky's complexity, and the oddness of his figures of speech, disappointing. But I kept coming back to him. Some of it still seems odd, stilted, but I suspect that some of this is due to translation difficulties. And some of the oddness disappears as I read more and learn his utterly original mode of thinking.
His poems are really growing on me. I would have said a month ago that my favorite is "The Butterfly"; but I find myself coming back again and again to "Lullaby of Cape Cod" and "Nunc Dimittis". "The New Jules Verne" is one of the funniest poems I've ever read. "Fin de Siecle"--about growing old (or, more accurately, growing unhealthy)--has just about the most meaningful ending, for me, of anything I've ever read.
I read "Lullaby of Cape Cod" twice today. I can't get its images out of my head: the loss of his home in Russia, what a hot Massachusetts summer night is like, all that can be learned from time and night, the fantasy of Atlantic codfish coming to the door--this is a poem about Cape COD, after all! The man does have a sense of humor-- with which he finally manages to lull himself to sleep.
This is the best book of his poetry. The translations are fairly consistent in tone, especially since he usually either translated them himself or advised those who did. If you buy it, be patient with it. Brodsky rewards patience.