This writeup makes many theological presuppositions which it does not itself defend at length. It is meant to be in the vein of hermeneutical and ecclesiological commentary.
It is common in cessationist and some pentecostal theologies to relegate tongues to the status of an "ecstatic experience". (I seem to recall that catholic theology has a similar bent, although I can't speak with any authority on that matter.) This does not seem to agree with the Pauline textual data. That is to say, if one's experience of tongues is ecstatic in a technical sense (loss of self-control, loss of the ability to apply reason to one's actions) then it seems outside the scope of what Paul was envisioning as he instructed the Corinthian church on this subject.
Gordon Fee's book on Pauline pneumatology, "God's Empowering Presence", and his commentary on I Corinthians, both deal with this issue extensively. In a nutshell, a primary line of Paul's argumentation is as follows:
You are flaunting the gift of tongues and not conditioning or controlling its use (or the broader use of spiritual gifts]) with the ruling virtue of love/agape (1 Corinthians 13), the reasonable application of which suggests that when you gather it is more valuable for something to be said which is intelligible to the unbeliever (1 Corinthians 14:19) than something which is only edifying to yourself (1 Corinthians 14:4), i.e., an uninterpreted tongue.
Therefore it is preferable to prophesy, and the public use of tongues should be accompanied by interpretation (1 Corinthians 14:1,5).
Furthermore, whether prophecy or tongues or anything else, everything should be done decently (14:40) and in accord with love, because "the spirits of the prophets are subject to the prophets (14:27-32)."
So it seems pretty clear that Paul did not have in mind the sort of flighty and freaky spiritual experiences that are often reported (or caricatured) when this subject is discussed, but rather something which was a deliberate exercise of a God-given ability (such an interpretation harmonizes with his exhortation in 2 Timothy 1:6 to "stir up the gift of God").
Having said that, is this grounds to condemn all ecstatic tongues experiences as ungodly? Well, not necessarily. First, notice that in this passage Paul is addressing the church when gathered as such; the metric of "what an unbeliever will think" clearly does not apply when you are in your prayer closet. Also notice that Paul does not waver as to the source of the gifts - they are God's gift to man (and woman1), even when they are abused and mis-practiced. So perhaps it would be more fruitful to read this as a commentary upon the maturity (or exigetical sophistication?) of the ecstatics, and to treat them accordingly (Romans 14).
In any case, the fact that pentecostal/charismatic phenomena have become a topic of serious theological discussion and exigetical/hermeneutical analysis in recent decades suggests that the holy rollers may not have been quite so far off the mark as was once thought.
1
See Joel 2:28-29 and its reference in Acts 2 both mentioning "daughters"; also presumed by 1 Corinthians 11:5, although there are other interesting issues regarding gender in view in that verse.