The Apostle Paul wrote that Christians should "put away" anger (Eph. 4:31), and in his letter to the Church at Colosse, he wrote that we are to "put off" anger (Col. 3:8). He also cautioned fathers not to provoke their children to wrath (Eph. 6:4), or to anger (Col. 3:21). In Ecclesiastes, we are told that "anger rests in the bosom of fools" (7:9), and in Proverbs, we read that "wrath is cruel, and anger is outrageous" (27:4). From these examples, one would certainly draw the conclusion that anger is an ungodly characteristic. But, as with every teaching from the Scriptures, we must take the whole counsel of God's Word.
There are some very revealing numbers concerning the words "anger" and "angry" in the Bible. "Anger" appears 224 times, and "angry appears 36 times in the Old Testament, but the two words have a combined total of only 12 times in the New Testament. Ironically, the majority of times they are used in the O.T., they refer to God's anger, usually at His chosen people, Israel! Here are just a few examples from Psalms: 7:11; 76:7; 79:5; 80:4; 85:5; etc. And on one occasion, Jesus was angry with His critics (Mk. 3:5).
God's anger toward Israel is quite understandable. The LORD had freed them from Egyptian bondage, fed them for forty years in the wilderness, given them His Law, given them their own land, and protected them from their enemies. When they turned to idol worship, He had every right to be angry with them. And, just as a human father gets angry when his child knowingly disobeys, and he punishes him, God also disciplines His children (Heb. 12:3-15). But unlike most men, God allows time for His child to repent and submit to His authority before taking punitive action. The phrase, "slow to anger" appears seven times in the Bible. Five of them describe God (Neh. 9:17; Ps. 103:8; 145:8; Joel 2:13; Jon. 4:2; Nah. 1:3), and the other two encourage men to be like Him (Prov. 15:18; 16:22). In the case where Jesus was angry, His anger was also aimed at the Jewish leaders (Mk. 3:5).
I believe Christians are to make certain that their anger is justified (Matt. 5:22), and then deal with it properly (Matt. 18:15-17). Of course, the better way is to forgive the person (Matt. 11:25). Forgiveness is a product of love, and we know that love is long suffering and bears all things (1 Cor. 13:4-7). Also, it is in our best interest to deal with the problem quickly, because otherwise, it could fester and become more serious (Heb. 12:15). If you must be angry, "Be ye angry, and sin not; let not the sun go down upon your wrath" (Eph. 4:26). If you are angry, deal with it!