God Remembered Noah
But God remembered Noah, and all the undomesticated animals, and all the domestic animals, that [were] with him in the ark. And God caused a wind to pass over the earth, and the waters subsided. — Genesis 8:1, my translation
The Hebrew word here for "remember" is זָכַר (zā-KHAR). The basic meaning of the word is "to call to mind" similar to our English word "remember". But often the word is practically a synonym for action, usually based on some obligation.
O LORD, you know; *remember* me and visit me, and take vengence for me on my persecuters. — Jeremiah 15:15 (ESV)
Jeremiah was faithful to God's Word and cause, and consequently was scorned and persecuted. Jeremiah calls on the LORD to vindicate him and to fight for him against those who persecuted him.
O LORD, I have heard the report of you, and your work [...] In the midst of the years revive it [...] make it known; in wrath *remember* mercy. — Habbakuk 3:2 (ESV)
Habbakuk prays that the LORD will show mercy to his people.
The people of Israel did not *remember* the LORD their God, who had delivered them [...] and they did not show steadfast love to the family of Jerubbaal [...] in return for all the good that he had done to Israel. — Judges 8:34-35 (ESV)
The context here is that the Israelites had begun to worship "the Baals" and "made Baal-berith their god." It is not that the existence of the true God was forgotten, as later chapters show, but that the Israelites failed to keep the promises they had made to worship only the LORD, and to obey all his commandments. This was egregious in light of the mercy God had shown in delivering them from the oppression of the Midianites.
Noah had seen God fulfill his promise to destroy the earth, and Noah had been lifted up above those waves of destruction in the ark that God had told him to build. But Noah was, well, not out of the water yet! If God did not do something, the ark would eventually become a tomb, as the cooped-up inhabitants starved to death, floating on the waterlogged wreck of a ruined planet. God had promised not simply to destroy the earth, but that Noah, his family, and the animals would be "saved alive". It logically followed that there had to be a restoration of the world as well, so life could continue. So God sent a wind to dry up the earth, and began lowering the water levels. As Dr. Gill put it:
Not a stormy blustering [wind], that would have endangered the ark, but a gentle, hot, drying one [...] It was, as the Targums of Jonathan and Jerusalem call it, 'a wind of mercies', or a merciful wind; or a wind of comforts, as Jarchi; for so it was to Noah and his family, and to all the creatures, since it served to dry up the waters of the flood, and caused them to subside.
As Christians, we have placed all our trust and hope in the Christ, and we have seen a certain measure of God's power, in changing us and delivering us from the power of sin. Yet, the bulk of what we hope for is yet future. Our faith would prove empty and pointless, if God does not some day do the rest of the things he has promised, specifically, to (1) give us new bodies which are free from corruption and the taint of sin; (2) judge and remove the wickedness of the world; and (3) heal the world and set up his own blessed, eternal kingdom. We are still very much in need of God's mercy, and we wait longingly for God to "remember" us and fulfill his promises.
 See HALOT.
 In the prophetic timeline, we await (1) the rapture of the church, (2) the seven year tribulation, (3) the establishment of the millenial kingdom, and then (4) the creation of a new heaven and a new earth.