I am disappointed with the status of unarmed combat in Minecraft. No one engages in hand-to-hand combat by throwing their right fist over and over and jumping around a bit.
My suggestion is this: You could enter a boxing stance by pressing "u" on a computer or holding both L2 and R2 (RB and LB on Xbox) on console, deselecting your hotbar entirely and raising your fists up like they are when you hold up a map. Pressing the left mouse button throws punches with alternating fists doing 4 damage, while the right brings your fists up to block, reducing damage by 25%, except for potions of harming.
In addition, punching through glass blocks or panes in a boxing stance would damage anyone behind them by 5 health points (due to glass shards), but damage the puncher by 3 (due to punching glass). Sprinting continuously for three seconds before an attack would double your knockback.
When moving in boxing stance, the more armor you have on, the slower you will move, except for leather armor. Each piece of Gold/Iron/Chainmail armor you're wearing will slow you down by 10%, while each piece of diamond will slow you down by 20%.
This would be useful for any time your sword breaks; I just suggested it because I like punching things, though.