Why did Morgoth curse Hurin instead of killing him?

Question

Why did Morgoth curse Hurin instead of killing him? Was it because he knew that if he killed him he would never be able to find Gondolin?

Answer 1

It was probably a combination of two factors:

• Cruel revenge As DVK pointed out in a comment on the question, Húrin's fate was an extremely cruel torture; Morgoth placed a curse on Húrin's entire family, and then forced him to watch it play out (emphasis mine):

  Therefore Húrin was brought before Morgoth, for Morgoth knew that he had the friendship of the King of Gondolin; but Húrin defied him, and mocked him. Then Morgoth cursed Húrin and Morwen and their offspring, and set a doom upon them of darkness and sorrow; and taking Húrin from prison he set him in a chair of stone upon a high place of Thangorodrim. There he was bound by the power of Morgoth, and Morgoth standing beside him cursed him again; and he said: 'Sit now there; and look out upon the lands where evil and despair shall come upon those whom thou lovest. Thou hast dared to mock me, and to question the power of Melkor, Master of the fates of Arda. Therefore with my eyes thou shalt see, and with my ears thou shalt hear; and never shalt thou move from this place until all is fulfilled unto its bitter end.'

  ^{_{The Silmarillion III Quenta Silmarillion Chapter 20: "Of the Fifth Battle: Nirnaeth Arnoediad"}}

  Húrin has to watch the story of Túrin Turambar, one of the most gut-punchingly horrifying tragedies in The Silmarillion, play out. And many of the main actors are his friends and relatives.

• He still wants to find Gondolin. It seems reasonable for Morgoth to assume Húrin would want to return to Gondolin after this long torture, and he set spies on Húrin with this purpose in mind (emphasis mine):

  Thus his freedom did but increase the bitterness of Húrin's heart; and he departed from the land of Hithlum and went up into the mountains. Thence he descried far off. amid the clouds the peaks of the Crissaegrim, and he remembered Turgon; and he desired to come again to the hidden realm of Gondolin. He went down therefore from Ered Wethrin, and he knew not that the creatures of Morgoth watched all his steps

  [...]

  For Húrin stood in despair before the silent cliffs of the Echoriath, and the westering sun, piercing the clouds, stained his white hair with red. Then he cried aloud in the wilderness, heedless of any ears, and he cursed the pitiless land; and standing at last upon a high rock he looked towards Gondolin and called in a great voice: 'Turgon, Turgon, remember the Fen of Serech! O Turgon, will you not hear in your hidden halls?' But there was no sound save the wind in the dry grasses. 'Even so they hissed in Serech at the sunset,' he said; and as he spoke the sun went behind the Mountains of Shadow, and a darkness fell about him, and the wind ceased, and there was silence in the waste.

  Yet there were ears that heard the words that Húrin spoke, and report of all came soon to the Dark Throne in the north; and Morgoth smiled, for he knew now clearly in what region Turgon dwelt, though because of the eagles no spy of his could yet come within sight of the land behind the Encircling Mountains. This was the first evil that the freedom of Húrin achieved.

  ^{_{The Silmarillion III Quenta Silmarillion Chapter 22: "Of the Ruin of Doriath"}}

Húrin's freedom also causes some other mayhem, such as the slaying of Thingol, which in turn leads to the downfall of Doriath and the sundering of Elves and Dwarves, but it's not clear whether or not Morgoth knew these things would happen. It's certainly possible, in which case it provides yet another motive, but we can't be certain.