I attended a small baptist church where tongues was rarely used for its actual purpose (delivering prophecy or undeniable message from God). However, it was somewhat common that when group prayer got very intense someone would utter a sentence or two in what sounded like a different language.
The pastor told me that they were prayer languages (see this study). They do not serve a purpose for anyone except the one praying; no translation is required. They are the most intimate prayers that can be given while on earth.
He gave me a few verses that support the idea:
1 Follow the way of love and eagerly desire gifts of the Spirit, especially prophecy. 2 For anyone who speaks in a tongue does not speak to people but to God. Indeed, no one understands them; they utter mysteries by the Spirit. 3 But the one who prophesies speaks to people for their strengthening, encouraging and comfort. 4 Anyone who speaks in a tongue edifies themselves, but the one who prophesies edifies the church. 5 I would like every one of you to speak in tongues, but I would rather have you prophesy. The one who prophesies is greater than the one who speaks in tongues,[c] unless someone interprets, so that the church may be edified. 1 Cor 14
The chapter goes on to say that tongues are acceptable (verse 18), however, many times less important than prophecy.
Finally, of course, there is Romans 8:26:
In the same way, the Spirit helps us in our weakness. We do not know what we ought to pray for, but the Spirit himself intercedes for us through wordless groans.
The logic is pretty easy to infer here. A prayer language is spoken when your own words cannot suffice. When you cannot express truly the "groanings" of your heart the Spirit may intercede and "groan" on your behalf.
The pastor and the congregation were passive about them and never really discussed them or boasted about them occurring to them or another. If it happened, that was fine; if it didn't, that was fine too.