What is the name of the legendary sword wielded by Arthas?

The legendary sword wielded by Arthas is Frostmourne. It is a cursed runeblade that transformed Arthas Menethil from a human paladin into the Lich King's most powerful death knight.

Arthas discovered Frostmourne in Northrend while pursuing the dreadlord Mal'Ganis during the events of Warcraft III: The Frozen Throne. Despite warnings from Muradin Bronzebeard, Arthas pulled the sword from its icy prison. The weapon killed or apparently killed Muradin, stole Arthas's soul, and gave him the power to defeat Mal'Ganis.

Frostmourne's curse made it far more than an ordinary magical weapon. It could consume the souls of those it killed, and the Lich King could communicate through it. After taking the sword, Arthas returned to Lordaeron and murdered his father, King Terenas, beginning his final descent into villainy.

Frostmourne is often confused with Ashbringer, the holy sword associated with Tirion Fordring, or Shadowmourne, a later weapon created during the campaign against Arthas. Frostmourne was destroyed by Ashbringer when the Lich King was defeated in Icecrown Citadel.