In Massie's book, Nicholas and Alexandra, he states that Rasputin had no desire for money or power, but only to continue living out his debauched lifestyle.
If that was the case, why did Rasputin help the Imperial Family in easing Alexei's hemophilia symptoms? I doubt it was out of sympathy as I believe that he was evil.
Perhaps to boast about gaining such favor with the tsar of Russia to (who else?) women? Maybe Rasputin told women that if they, um, granted his favors, then he could persuade the tsar to make decisions that they wanted? That really is all I can think of, but I know there definitely could be more solid theories out there.
Suggestions?