Almost nothing was accurate. The actual group was an Islamic sect that was publicly known. They used daggers often for murders but they also used actual armies in battle. They only existed in the Middle East.

The Templars are also almost unrelated to their historical counterparts.

Assassin's Creed has fun with history but ignores anything that doesn't fit the story.

The Assassin costume featured in the games appears to have been inspired by a description from Idries Shah's (under the pen name Arkon Daraul) A History of Secret Societies. Here is the quote in question:

"The victim having been pointed out, the faithful, clothed in a white tunic with a red sash, the colors of innocence and blood, went on their mission without being deterred by distance or danger. Having found the person they sought, they awaited the favorable moment for slaying him, and their daggers seldom missed their aim.”

Given the book's popularity in conspiracy theorist circles (it was frequently cited by the late ufologist/conspiracy theorist Milton William Cooper, author of Behold a Pale Horse and host of the radio broadcast The Hour of the Time) I feel confident in dismissing it as pseudohistory.

edit: Here's a link to a recording of Cooper's radio show. This particular broadcast consists almost entirely of Cooper reading the section from Shah's book about the assassins.