Armor

While armor is clearly worn by Guards throughout Assassin's Creed, it is unknown if Altaïr wears any.

On Altaïr

Altaïr does have gloves, boots etc. that appear to be made of leather, but it is unknown if he wears any actual metal armor underneath his robes. It is never mentioned, never seen, never upgraded during the game. One argument in defense of the theory that he wears armor is that in combat, Altaïr can take great amounts of damage without dying. This, however, is most likely because of Synchronization. Desmond, in the Animus, is able to take damage. However, the real Altaïr may have been too great a fighter to take any damage. So, when Desmond in the Animus takes damage, he loses Synchronization with the actual events.

This does nothing to make the idea that Altaïr wears armor unlikely, it only explains a very common argument in defense of the idea that he does. He may wear armor. However, if he does, it is most likely lightweight leather or chainmail armor, because platemail is very bulky and cumbersome, making the acrobatic moves Altaïr performs certainly impossible.

On other characters

Armor does appear on other characters in the game, and there are differences in the styles worn by guards in each city. The guards in Damascus can be found in either lamellar, likely leather, or ringmail armor. Guards in Acre can be found in brigantine armor and chain mail, some complete with coifs. Guards in Jerusalem are often found wearing scale or splintmail. Each of these guard types can be found in the Kingdom near their respective cities. The Knights Templar uniformly wear full suits of chain mail covered in a white tabbard with a red steel helm covering their face.