The Weapon that does the most damage in the whole game is the Star Cannon (http://terraria.wikia.com/wiki/Star_Cannon), however because of its unreasonable amount of Fallen Stars (http://terraria.wikia.com/wiki/Fallen_Star) to be used as amunition, the Fiery Greatsword comes in first with its constant supply of damage (http://terraria.wikia.com/wiki/Fiery_Greatsword).
Hope I helped :)
The weapon that does the most damage is the Night's Edge
It does 40 damage and is the same speed as the Fiery Greatsword
http://www.youtube.com/watch?v=DVsFGcW05eU&feature=player_embedded
Heres a video of how to make it