Cessationists Position-Not based upon Scripture
Cessationists believe the supernatural gifts found in 1 Cor 12 & 14 have ceased and in Ephesians 4:11. They say these gifts ceased after the time frame of the Book of Acts, since 70AD, or completion of the Cannon. The problem is there is no Bible verse or passage of Scripture to defend this position-NOT ONE. In order to defend their position scripturally they must manipulate and twist Scripture. Most Cessationists come from a strong Reformed Theology that does not believe in dispensationalism, and focuses on the destruction of the temple in 70AD.

Continuationist Position-Based Upon Scripture
Ephesians 4:11-13
11 So Christ himself gave the apostles, the prophets, the evangelists, the pastors [shepherds] and teachers, 12 to equip his people for works of service, so that the body of Christ may be built up 13 until we all reach unity in the faith and in the knowledge of the Son of God and become mature, attaining to the whole measure of the fullness of Christ.
We currently do not have that unity. The body of Christ is certainly not mature, far from it. The body of Christ today is certainly not obtaining the whole measure of the fullness of Christ. Thus, there is still the need of the Five Fold Ministry. There is no Bible passage that says there is the need of the Evangelists, Pastors, and Evangelists and not the Apostles and Prophets. (Some consider the Apostle similar to Church Planter or Missionary-no Bible passage to defend this position.)

1 Corinthians 1:5-7
5 that you were enriched in everything by Him in all utterance and all knowledge, 6 even as the testimony of Christ was confirmed in you, 7 so that you come short in no gift, eagerly waiting for the revelation of our Lord Jesus Christ,
Almost all Christians would agree that Apostle Paul is speaking of the Second Coming of Jesus. Paul mentions not coming short in any gift. In 1 Corinthians 12, 13, and 14 he addresses the gifts of the Holy Spirit. Thus, Apostle Paul certainly was not a cessationists, far from it.

1 Corinthians 13:8-11
8 Love never fails. But whether there are prophecies, they will fail; whether there are tongues, they will cease; whether there is knowledge, it will vanish away. 9 For we know in part and we prophesy in part. 10 But when that which is perfect has come, then that which is in part will be done away. 11 When I was a child, I spoke as a child, I understood as a child, I thought as a child; but when I became a man, I put away childish things. 12 For now we see in a mirror, dimly, but then face to face. Now I know in part, but then I shall know just as I also am known.
Obviously that which is perfect has not come-it will not come until we receive our glorified bodies at Jesus' return. When Jesus returns nothing will be dim. When will we know just as we are known, when Jesus returns.

1 Corinthians 12:27-31
27 Now you are Christ’s body, and individually members of it. 28 And God has appointed in the church, first apostles, second prophets, third teachers, then miracles, then gifts of healings, helps, administrations, various kinds of tongues. 29 All are not apostles, are they? All are not prophets, are they? All are not teachers, are they? All are not workers of miracles, are they? 30 All do not have gifts of healings, do they? All do not speak with tongues, do they? All do not interpret, do they? 31 But earnestly desire the greater gifts. And I show you a still more excellent way.
Earnestly desire the gifts, until 70AD or the canonization of the Bible? (No such passage.) Some argue the more excellent way is not having the gifts after the canonization of Scripture, but the more excellent way is 1 Corinthians 13-love.
All must agree there is absolutely no hint of the canonization of the Bible in the mind of any of the Bible writers. Just the opposite based upon 2 Timothy 3:16, All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness. Most importantly Almighty God knew there would be the canonization of Scripture, but he never mentions it in the Old Testament or New Testament.

Acts 4: 29
And now, Lord, consider their threats, and enable Your servants to speak Your word with complete boldness, You stretch out Your hand to heal and perform signs and wonders through the name of Your holy servant Jesus.
Where in Scripture does it say that God no longer wants to use followers of Jesus in healing, signs, and wonders. Especially in today's culture where Satan is more active than ever. Does God only want Satan's false signs and wonders (the counterfeit) on earth?

Partial Cessasionist-Actually Cessationists Overall
There are those who say they are not cessationists however their interpretation of the gifts of the Holy spirit lean towards not seeing the gifts as supernatural gifts of the Holy Spirit. They see the gifts of knowledge and wisdom as someone having great insights and wisdom, whereas these two gifts are supernatural gifts not based upon how learned a person may be. Almost all do not believe that there is the gift of healing in a supernatural realm, as in individuals having the ability to heal people by the power of the Holy Spirit as seen in the Book of Acts. They certainly do not believe God can gift a person to perform miracles in a supernatural manner. (Take note that other than healing miracles very few miracles took place in the New Testament.) Most believe tongues is a known language even though the Bible calls it an unknown language. They say the tongue is unknown to the speaker but Scripture shows that is not the only use of tongues.