This verse contains the first mention of the beautiful word "remember" in the Bible, and it tells us that God remembers! During the awful cataclysm of the Flood, the most devastating event thus far in the history of the world, God still remembered the faithful obedience of Noah, and He even remembered every living thing!
We may forget many things, but God remembers: "For God is not unrighteous to forget your work and labour of love, which ye have shewed toward his name" (Hebrews 6:10). Nor does He ever forget a promise. The first mention of "remember" in the New Testament is the Spirit-inspired testimony of Zacharias: "Blessed be the Lord God of Israel; for he hath visited and redeemed his people . . . to remember his holy covenant; The oath which he sware to our father Abraham" (Luke 1:68, 72-73). That promise had been made 2,000 years before, but God remembered.
God even remembers the sparrows: "Not one of them is forgotten before God" (Luke 12:6). And He certainly remembers His own children: "For he knoweth our frame; he remembereth that we are dust" (Psalm 103:14).
Even after the children of Israel had gone deeply into idolatry, He could still say, "I remember thee, the kindness of thy youth, the love of thine espousals, when thou wentest after me in the wilderness" (Jeremiah 2:2).
God remembers the evil as well as the good, of course. The one thing He chooses not to remember is the sinful past of those who have come to Christ for forgiveness. "And their sins and their iniquities will I remember no more" (Hebrews 10:17). HMM