I'm trying to think of a single thing in that game that is accurate. Some of the architectural reproductions in the series are impressive, but even that is wrong in places (usually location.)

Historically the actual "assassins" were the military corps of a Shia splinter group, the Nizari Ismailis who set themselves up in a number of fortresses throughout the middle east, most notably Masyaf and Alamut. They did carry out a number of assassinations, the act and their name probably referring to the idea that their agents consumed hashish. That is widely thought to be a legend, however as there is no supporting evidence of it. This assassin corps would have referred to themselves as fedayeen, ones who sacrifice.

"The Assassins" as an extra-national independent group were basically wiped out by the Mongols who were unwilling to tolerate the continued existence of such a threat, but the Nizari Shia still exist and still have an Imam, who is today called the Aga Khan. Far from going around assassinating people the current Aga Khan is a wealthy philanthropist devoted to eliminating poverty, and promoting secular pluralism, but that's obviously getting into 20 year territory.

edit: source wise, see the Encyclopedia of Islam entries on Nizariyya, Fidai, and Hasan-i Sabah.