No. In fact, Arthas never died. He was still alive at the start of the WC3 undead campaign, and when he fused with the Lick King, it was their souls that came together.L.B. Jeffries said:This might be a stupid question but has anyone killed Arthas or anything like that? Do people do that in WoW?
In warcraft lore, the only antagonists remaining are Arthas, Kil'jaeden, Sargeras, and the other old gods. Arthas will probably be killable in a patch for the new expansion, but it will probably mark the end of the expansion's content. I think this, or the next expansion blizzard makes, will be the end of WoW.