Reportedly it took poison, falling down a staircase, and repeated gunshots before Rasputin was finally dead. It's said that Rasputin mumbled a curse from his deathbed, assuring Russia's ruling monarchs that they would all be dead within a year. That did come to pass, as the Romanov family was brutally murdered in a mass execution less than a year later.
I thought I also heard that an additional part of the curse was that Russia would never be ruled again by the Romanovs. That has also come to pass.