What is the consensus among Reformed Christians regarding spiritual gifts? Here’s a summary along with some biblical reasons.
Most Reformed theologians have held that the Spirit grants extraordinary gifts as miraculous confirmations of major transitions in redemptive history, such as changes to the structure of covenant life or whenever fresh revelation is added to Scripture. During apostolic times, for instance, the Spirit gifted people with a supernatural ability to speak unlearned human languages (i.e., "tongues"), to heal upon command, foretell future events, and compose scripture. These unusual gifts served as signs certifying God’s hand in these momentous changes. Because we are no longer in such a period of transition, we should not expect extraordinary gifting to occur, any more than we look for new apostles or additions to the Bible.
The confirmatory nature of extraordinary gifts in the New Testament is highlighted by an often overlooked fact. The Bible provides no instance of the Spirit having ever granted them to anyone apart from the presence of an apostle, whose authority the gifts served to confirm. A key text demonstrating this is Acts 8:14-20:
Now when the apostles at Jerusalem heard that Samaria had received the word of God, they sent to them Peter and John, 15 who came down and prayed for them that they might receive the Holy Spirit, 16 for he had not yet fallen on any of them, but they had only been baptized in the name of the Lord Jesus. 17 Then they laid their hands on them and they received the Holy Spirit. 18 Now when Simon saw that the Spirit was given through the laying on of the apostles’ hands, he offered them money, 19 saying, “Give me this power also, so that anyone on whom I lay my hands may receive the Holy Spirit.”
Note, the text describes how certain Samaritans had come to faith and were baptized, yet in order for these believers to receive sign-gifts it was necessary for apostles to be dispatched from Jerusalem. Only after Peter and John had come to them in person did the Spirit pour out the gifts. The implication, which Simon Magus seems to have clearly understood, is it was impossible to receive "the powers of the age to come" apart from having come into physical proximity with an apostle.
The purpose of such gifts, then, was primarily to testify to the unique authority which Christ conferred upon the apostles as founders of the New Covenant church and agents of special revelation. This understanding leads naturally to a conclusion: extraordinary gifts persisted in the church only as long as that first generation of Christians who received them among the apostles survived. Notably, this is exactly the situation which Augustine, writing in the fourth century, describes:
I said (chap. xxv), “These miracles were not permitted to last till our times, lest the soul should always seek visible things, and the human race should grow cold by becoming accustomed to things which stirred it when they were novel.” That is true. When hands are laid on in Baptism people do not receive the Holy Spirit in such a way that they speak with the tongues of all the nations. Nor are the sick now healed by the shadow of Christ’s preachers as they pass by. Clearly such things which happened then have later ceased. But I should not be understood to mean that to-day no miracles are to be believed to happen in the name of Christ. (Retractions 1,13)
With respect to the last sentence, Nathan Businitz observes,
Augustine’s miracle accounts do not involve miracle workers who possessed the gift of healing. Instead, these accounts are presented as unexpected and providential acts of God which were not dependent on an intermediary healer. In that sense, they are categorically different than the type of healing miracles that are described in the Gospels or the book of Acts. Nothing in Augustine’s account suggests that the “gift of healing” was involved in the episodes he recounted.
To be clear, the cessation of extraordinary gifts should not be misunderstood as discounting the ongoing work of the Holy Spirit. God continues to answer the prayers of believers for miraculous healing. He simply does so without, as Businitz put it, “an intermediary healer” who says authoritatively, “be healed!” Having withdrawn gifts suited to a transitional period in redemptive history, the Holy Spirit continues to empower believers today with diverse gifts for edification and mission such as preaching, teaching, administration, and—above all—love.
As for the "unknown tongues" mentioned by Paul in 1 Cor, I agree with the Reformed consensus. Paul should be understood as speaking rhetorically of the ability to speak angelic languages. His phrase, "though I speak in the tongues of men and angels," should not be taken as either confirming or denying the real possibility of speaking unknown or angelic tongues. Rather, he contrasts others' supposed boasting with the much higher place given to intelligible words spoken in love. To put it differently, Paul means, “even if I were able to speak every conceivable language, including that of angels, it wouldn’t matter if I did so without love.” Since this is the only text I’m aware of which can possibly be taken as referring to unknown tongues, it seems the doctrine of glossolalia as practiced by many charismatic churches sits on weak foundations.