Thanks for your inquiry! There is no more pervasive and pressing a question as this one, so it's wise to have a biblical perspective on the issue of "tongue-speaking."
Some denominations teach a "second baptism" of the Holy Spirit: one that causes believers to "speak in tongues." These denominations make speaking in tongues a mark of genuine Christianity -- or at least an indicator of greater faith in Christ. What's more, Christians of all denominations -- including Roman Catholic and Episcopal -- have professed to "speaking in tongues" in recent decades.
The Scripture that these so-called "charismatic" (or, as one theologian astutely observed, "neo-Pentecostal") Christians reference is Acts 2. When the eternal Spirit of God -- who has been present and active from before time as the third person of the Trinity -- was poured out in a new and powerful manner on the disciples at Pentecost, each person heard "every man in (their) own tongue, wherein (they) were born." Note first that the gift was one of HEARING, and that the disciples -- hailing from various regions and dialects -- were speaking known, recognizable languages.
What was the purpose of this "hearing in tongues?" Not long before Pentecost, the Lord Jesus Christ had ascended to the right hand of the Father after commissioning the apostles to "make disciples" of every nation. The followers of Christ now had a glorious message of salvation and of transformation to tell a dying world.
The problem was, they needed unity. They also needed empowerment so that they would be speaking the word of God and NOT the words of men. To that end, our gracious Lord sent His Holy Spirit in a more-powerful way than ever before to confirm the apostles through miraculous signs (such as healings), to change the hearts of sinful humans and to drive home the Word of Truth.
Part of the Spirit's work was to allow these disciples, from different dialects and areas, to understand one another: much as the United Nations today has translators to allow representatives from the various countries to understand each other's words. Work never would be accomplished at the U.N. if there were no translators, and the same priciple held true at the day of Pentecost.
Tongues, like the other "gifts of the Spirit," were for the early church period only. They enabled the nascent church to become organized and to spread the gospel of our Lord Jesus Christ to the nations. Once the disciples were on the same linguistic page, they could proclaim the message of grace to a hurting world.
It is interesting that the Apostle Paul taught that tongues would cease (I Cor. 13:8) and that the declaration of the Word of God was superior to tongues (I Corinthians 14 passim). St. Paul moreover encouraged the church to speak in a known language (I Cor. 14:19), and he said tongues were a sign not for believers but for unbelievers (I Cor. 14:23-26). This, the most-detailed discussion of tongues in the New Testament, obviously weighs heavily against the modern phenomenon of "speaking in tongues."
If one examines "tongues" in the church today, he will find that most professed "tongue-speaking" is nothing more than jibberish; those claiming to speak in tongues are not even speaking a recognizable language. Tongue-speakers most often feel pressured to "have an experience" in order to be a "real" Christian, thus their babbling is done out of compulsion and not for the edification of the Body of Christ.
There is no more speaking in tongues today, because the Holy Spirit has enabled us to translate the Scriptures into known languages and dialects and thereby to take the gospel message to all people. The church has been established and has no further need of the charismatic gifts of the Spirit. The Spirit's role today, actually, is to convict men of sin, to work faith and new life in Christ in the hearts of men, to strengthen Christians, to intercede for Christians and to guide Christians in living for God.
Those who claim to "speak in tongues" -- desiring the *gifts* of the Spirit -- would be wise to read the whole counsel of God regarding this matter, to desire the *fruit* of the Spirit (Galatians 5) and to "covet ... a more excellent way": the way of love in Christ.