ANSWER: God can and does change His mind, but only if people sincerely repent of their sins and respond by doing what is right. Sometimes He chooses not to punish someone after he has said that he would. Since he is merciful, He responds readily when people, with their whole hearts, repent. There are several examples in the Bible of God changing his mind or "repenting" of what he planned.
Perhaps the most well known change of mind occurred with Nineveh, the capital of the ruthless Assyrian Empire. When Jonah visited the city, he proclaimed repeatedly that in just forty days the city would be overthrown (Jonah 3:4). Unlike the hard-hearted inhabitants of Jerusalem on so many occasions, the pagan idolaters of Nineveh started to repent and put on sackcloth in order to humble themselves before God. They proclaimed a fast that even the king endorsed with a royal decree. His reason for the fast was the hope that the Lord would forestall the punishment they deserved (verse 9).
What was the response of God to those in Nineveh who humbled themselves? He saw what they did and decided in his mind to alter his plans. He decided not to destroy the city (verse 10)
A second interesting case of our Father deciding to reverse a previous decision is when King Hezekiah asked to live after he was told he would soon die (See 2Kings 20:1 - 11). Upon hearing the news, the king prayed and wept saying that he had served the Lord well. His prayer was heard and Isaiah was told to return to him to say that not only would he be healed, he would live another fifteen years (verses 5 - 6)! This example shows that we should pray even when a case seems hopeless since he can still choose to help us.
A third, rather striking example of a decision being reversed concerns King Ahab of Israel. Ahab (who married Jezebel) was the WORST king who ruled ancient Israel. A prophet no less than Elijah was sent to the king to warn him to repent and the consequences for not doing so (1Kings 16:30 - 33, 21:25)
One day Ahab wanted to buy a vineyard that was next to his palace. The owner (Naboth), however, refused to sell it. After hearing her husband whine about the vineyard, Jezebel arranged for the death of Naboth through false witnesses who would accuse him of blasphemy. After he was stoned to death, God sent Elijah to Ahab as the king was in Naboth's vineyard to make it his own. The king was warned that the punishment for his many, many sins was that he would soon die and that dogs would lick up his blood from the streets (1Kings 21:19, 21 - 22)!
After Ahab heard these words, he did something unusual that caused God to change his mind. The king took off his royal clothes, put on sackcloth, and mourned his sins (verse 27 - 29). His actions were seen from heaven and he was not punished!
This shows that even a notoriously wicked king can get God to change his mind. There are, of course, other examples of decisions being reversed. Although the Creator knows everything, he sometimes decides to alter his decisions IF people think and act differently in response to his warnings.