Hemophilia

Poisoned, shot four times, beaten, and drowned.

Rasputin: what a legend. The fact (rumor?) that it took poison, multiple gunshots, and finally a little bit of drowning to successfully murder him makes him seem almost supernatural. (Hey, remember that animated Anastasia movie?)

But on a more relevant note, Rasputin was also known for his role as the "healer" of Alexei Nikolaevich, Tsarevich of Russia. Alexei suffered from hemophilia, which is a bleeding disorder. In fact, a couple of royal descendants of Queen Victoria were hemophiliacs (oh those silly inbreeders, not that I'm judging). There are a variety of hemophilia disorders, but the two types of most significance are hemophilias A and B. 

Hemophilia A (the most common hemophilia) is an X-linked recessive disorder resulting in a deficiency of Factor VIII in the coagulation cascade. 

Hemophilia B is an X-linked recessive disorder resulting in a deficiency of Factor IX in the coagulation cascade. The deficiencies in factors VIII and IX will contribute to ineffective formation of fibrin (= ineffective clotting). 

Note that a common complication of hemophilia is hemophilic arthropathy, where there is bleeding in the joints that may result in joint deformities if left untreated.