FarBeyondC
Explorer
Unarmed attacks are weapons as they are listed in the weapons chart as simple weapons that don't cost anything do 1 point of bludgeoning damage and have no properties. P 149 PHB.
Just wanted to note that- as of the errata to the Player's Handbook, released on the 10th of June, 2015 and found here- Unarmed Strikes are no longer considered weapons and do not belong on the weapon table.