If God is all good, all knowing, and all powerful, how can suffering still exist?

At the risk of being overly simplistic, there are two things in play here. First, we need to understand that God created us with free will, in other words, with the ability to choose, to make choices, about ourselves and our lives. If we have the freedom of choice, the potential for evil exists because we can choose to follow God and do good, or to do life our own way and do evil. The fact is, without the freedom to choose, the concept of love is meaningless. As Christian apologist Hank Hanegraaff so colorfully said, “God is neither a cosmic rapist who forces his love on people, nor a cosmic puppeteer who forces people to love him. Instead, God, the personification of love, grants us the freedom to choose. Without such freedom, we would be little more than preprogrammed robots.” When God first placed Adam and Eve in the Garden of Eden, the Lord God commanded the man, “You are free to eat from any tree in the garden; but you must not eat from the tree of the knowledge of good and evil, for when you eat of it you will certainly die—Genesis 2:16-17. Two things become apparent: (1) Man was free to do what he wanted, and (2) he had the freedom to choose, complete with a warning of consequence if he chose wrong. Unless he had the freedom to be wrong, being wrong was not possible. Of course, as history records, Adam and Eve chose wrong, deceived by the serpent, and mankind has been choosing wrong ever since. As David rightly recorded, The fool says in his heart, “There is no God.” They are corrupt, their deeds are vile; there is no one who does good. The Lord looks down from heaven on the sons of men to see if there are any who understand, any who seek God. All have turned aside, they have together become corrupt; there is no one who does good, not even one—David, Psalm 14:1-3. Paul of course underscored that idea in the New Testament, telling the church at Rome, [F]or all have sinned and fall short of the glory of God—Paul, Romans 3:23. That is the magnificence of the work of Jesus Christ, who by His life, death and resurrection, provided complete victory over our inherent wickedness by His perfect life; as Paul noted, God made him who had no sin to be sin for us, so that in him we might become the righteousness of God—Paul, II Corinthians 5:21. That’s why, as Christ Himself noted to Nicodemus, I tell you the truth, no one can see the kingdom of God unless he is born again. . . . For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but to save the world through him. Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God’s one and only Son—Jesus Christ, John 3:3, 16-18. And as John the Baptist said in complete harmony with Christ, Whoever believes in the Son has eternal life, but whoever rejects the Son will not see life, for God’s wrath remains on him—John the Baptist, John 3:36. And the second thing in play here is that God, while being completely God, does limit Himself in His interactions with mankind. One area that we see that is in the area of natural laws—laws that God Himself created as an extension of His nature. As an example, let’s say a person falls out of an airplane without a parachute. God knows that person, loves that person and cares about that person. But, while He could, God will likely not perform a miracle—a suspension of His laws—in order to save that person. His law of gravity will dictate the result of that person’s fall (much as we watched in horror as people fell out of the World Trade Center towers on 9/11). In other words, sometimes suffering is the natural consequence of the forces of this world, and/or the natural consequences of our choices. Another, more amazing way, that God limits Himself is found in how the Bible records His forgiveness of our sins. God said this through the prophet Isaiah: I, even I, am he who blots out your transgressions, for my own sake, and remembers your sins no more—God speaking, Isaiah 43:25. And God goes on to say through Isaiah, I have swept away your offenses like a cloud, your sins like the morning mist. Return to me, for I have redeemed you—God speaking, Isaiah 44:22. The prophet Jeremiah celebrated the same message in another word from the Lord: For I will forgive their wickedness and will remember their sins no more—God speaking, Jeremiah 31:34b. Do you hear what’s being said? God, who knows all, is limiting His memory in the area of our sins. They are so forgiven, they are forgotten. King Hezekiah, in his words at how God dealt with his sins, said it this way: In your love you kept me from the pit of destruction; you have put all my sins behind your back—King Hezekiah, Isaiah 38:17b. Another incredible picture of how God deals with our sins is found in the words of King David, who said, The Lord is compassionate and gracious, slow to anger, abounding in love. He will not always accuse, nor will he harbor his anger forever; he does not treat us as our sins deserve or repay us according to our iniquities. For as high as the heavens are above the earth, so great is his love for those who fear him; as far as the east is from the west, so far has he removed our transgressions from us—David, Psalm 103:8-12. What an amazing picture of how far God separates us—and Him—from our sins. And one of the most amazing pictures of God’s limiting Himself regarding us is found in the last book of the Bible, in the words of Christ: Here I am! I stand at the door and knock. If anyone hears my voice and opens the door, I will come in and eat with him, and he with me—Jesus Christ, Revelation 3:20. We’re talking about the One in whom, according to Paul, all the fullness of the Deity lives in bodily form—Paul, Colossians 2:9. Jesus could blow the door down—but instead, He waits outside, quietly knocking, waiting for us to answer and invite Him in. That’s love, and grace, and incredible! So suffering does exist because our choices have created that opportunity for suffering to exist, and because God in the course of fulfilling His plans, will often allow pain and suffering and heartache to turn our attentions to Him. As C.S. Lewis so brilliantly pointed out, “Pain insists upon being attended to. God whispers to us in our pleasures, speaks in our consciences, but shouts in our pains. It is his megaphone to rouse a deaf world.” Or, as Paul noted to the church in Rome, And we know that in all things God works for the good of those who love him, who have been called according to his purpose—Paul, Romans 8:28. And Jesus Himself, who certainly endured pain and suffering during His time on earth, said this to His disciples in some of His final words to them while in the Upper Room (just prior to Gethsemane): I have told you these things, so that in me you may have peace. In this world you will have trouble. But take heart! I have overcome the world—Jesus Christ, John 16:33. And the disciple who recorded those words reiterated those same thoughts in his first letter, sharing with his audience, [T]he one who is in you is greater than the one who is in the world—I John 4:4b.
Finally, as we close this question, we cannot forget that this world, for all that it is, is temporary. There is an eternity awaiting all of us in Christ—with a joy that will never be changed, will never be diminished. As John reported in his vision of what was to come, Then I saw a new heaven and a new earth, for the first heaven and the first earth had passed away, and there was no longer any sea. I saw the Holy City, the new Jerusalem, coming down out of heaven from God, prepared as a bride beautifully dressed for her husband. And I heard a loud voice from the throne saying, “Now the dwelling of God is with men, and he will live with them. They will be his people, and God himself will be with them and be their God. He will wipe every tear from their eyes. There will be no more death or mourning or crying or pain, for the old order of things has passed away.” He who was seated on the throne said, “I am making everything new!” Then he said, “Write this down, for these words are trustworthy and true”—Revelation 21:1-5. There is a day coming where all suffering, pain and evil will be forever gone. That is God’s promise, and our inheritance in Christ.