Fist

Fists were the weakest form of fighting, useful when no weapons were available, or when an Assassin did not wish to draw the attention of a guard.

High Middle Ages
Altaïr Ibn-La'Ahad could use his fists to fight or stun enemies at any time, though they were quite ineffective against alerted or armed opponents.

Novice Assassin were not yet allowed to carry weapons, and thus needed to avoid fights, or resort to their fists. Higher-ranked Assassins also used unarmed fighting to interrogate a target, or after being caught by thugs while attempting to pickpocket throwing knives.

Using fists in a fight against civilians did not raise suspicion with the guards, who would only intervene if they themselves were attacked.

Renaissance
Ezio Auditore da Firenze was more skilled in fistfighting than Altaïr, and was likely taught by his brother, Federico. The two were once embroiled in a brawl against Vieri de' Pazzi and his men, where all present used only their fists.

When unarmed, Ezio could perform many different combination strikes, counter other fist fighters, and throw sand in their faces. He also learned to disarm foes and use their weapons against them; eventually learning to kill them in one swift move right after doing so. It is to be noted, however, that you can not chain together kills with your fists like you do with the other melee weapons.

Fists also became a more viable option for combat when the Metal Cestus, a hard steel hand-guard, was purchased from a blacksmiths.

Guards eventually learned to throw sand in Ezio's face, exactly as he could, though they could do so while still holding onto their weapons. Ezio could only perform the same move with his weapon equipped, as long as he had no bullets or throwing knives left.

Additionally, the Caserma di Alviano played host to a Fight Club, where mercenaries competed in unarmed fighting. Ezio was able to participate in the fights, by Bartolomeo d'Alviano's suggestion, in order to improve his skills with his fists.

Modern Times
Upon escaping Abstergo Industries with Lucy Stillman, Desmond Miles did not yet have a weapon, and was thus forced to fistfight the Abstergo security officers attempting to detain him.

Though his abilities were initially rather limited, over time, he was able to gain Ezio's fistfighting skills through the Bleeding effect. After this, he became able to perform counters and disarm his enemies.

Trivia

 * Without the Metal Cestus, Ezio's fists will only have 1 damage, 5 speed, and 1 counter. The Metal Cestus boosts the damage stat to 3.
 * You can earn the "Messer Sandman" achievement by throwing sand at four guards at once; a skill that can be learned from the instructor at Monteriggioni.
 * When Ezio picks up a body, the fists will automatically become selected.
 * When Ezio successfully disarms a guard and continues to use his weapon, the icon at the bottom left hand of the screen will remain as the fist icon.
 * Despite seemingly lethal actions, such as attacks where Ezio cracks his target's neck, targets defeated with fists will merely appear to be in a subdued state, and will not be counted as dead.
 * If Ezio tries to pick up an unconscious victim and throw them off a building or cliff, they will still not be counted as dead.
 * In Assassin's Creed: Revelations, however, particularly during missions where full synchronization requires Ezio to not kill anyone, knocking out a guard using fists will still count as a kill.
 * In the Assassin's Creed II memory "Last Man Standing," it is possible to disarm the attacking Brutes, but not the normal guards. Nevertheless, this gives the chance to use the stolen weapon to defeat all guards.