The Raskolniki, as has been mentioned above, were (in a way, are) a group of Russian Orthodox who refused to accept Patriarch Nikon's reforms
Their chief difficulty was the fact that among them numbered no bishops. Thus, they were unable to replace their priests and at the same time, follow Church laws--a bishop is required to ordain new clergy members. One sect of Raskolniki, the Bezpopovzi (those-without-priests), dealt with this by wholly abolishing the hierarchy.
One group of them, known as the Belokrinitzians, survive, but they are not accepting of new members. They found a bishop (from the parish of Belaya Krinitza in the modern-day Czech Republic) who was willing to ordain one of their number a bishop, but there was some controversy over the validity of the Czech's own baptism.
The author Lev Tolstoy is known to have financially and otherwise supported a sect known as the Beguny("runners"; they would literally run from village to village fleeing the Tsar's agents), to assist them in fleeing to Canada, where their descendants remain.