The Westminster Shorter Catechism says that "[God] is a spirit, whose being, wisdom power, holiness, justice, goodness, and truth are infinite, eternal, and unchangeable." Those things do not change. A number of Scriptures attest to this idea (such as Num. 23:19; 1 Sam. 15:29; Ps. 102:26; Mal. 3:6; 2 Tim. 2:13; Heb. 6:17–18; Jam. 1:17) 
God's immutability defines all God's other attributes: God is immutably wise, merciful, good, and gracious. The same may be said about God's knowledge: God is almighty (having all power), God is omnipotent (having all power), God is omnipresent (present everywhere), God is omniscient (knows everything), eternally and immutably so. Infiniteness and immutability in God are mutually supportive and imply each other. An infinite and changing God is inconceivable; indeed, it is a contradiction in definition. 
While most Judeo-Christians believe that there are aspects of God that do not change, opponents believe that the benevolence of God is often expressed through his willingness to change his promised course of action which implies a certain level of mutability. (See Exodus 32:14 and Numbers 14:12-20; Jonah 3:10; Amos 7:3-9; Jeremiah 26:3)
For example, when God was giving the law and the Ten Commandments to Moses, he was gone for so long that Aaron, his brother the high priest, and the people, thought that he was dead or that something had happened, and the people asked Aaron to build them the Golden Calf. On that occasion, and during another when the people rebel against Moses and God, God threatens to destroy the people and make a nation out of Moses alone, but Moses reminds God of the promise he made to Abraham to make Israel a great nation, and the earlier promise to Noah not to wipe out all human beings ever again until time's end. God relents, but says that all those who participated will not be allowed to enter Canaan, the promised land.
It could be said that God knows beforehand all the possible steps each creature- i.e., each human, could take at any given moment, whether good or bad, and God also knows beforehand from eternity what he will or will not ultimately do in any given situation, knowing that sometimes he will say he is going to do something worse, and then doing either a less negative response or nothing at all. This allows God to exhibit a unique form of free will, and to show his mercy an forgiveness and holiness- qualities God values.