My mind quickly flashes to the stereotypical Pentecostal parishioner with his arms in the air, meaningless babble spewing from his lips while people around him scream "HALLELUJAH!" I haven't ever been to a Pentecostal service, though. Do speakers speak to each other in tongues, holding conversations, or is everyone just shouting out whatever the heavenly radio waves feel like sending out on a given day?
Either way, I doubt this is really what the gift Paul talks about consisted of. Linguists who have studied Pentecostal glossolalia (a fancy word for 'speaking of tongues') claim that the sounds made by practitioners don't seem to follow any sort of language structure, bear no resemblance to any living or dead language, and the sound is often heavily influenced by the speaker's native tongue. Given this, I have a hard time believing that those Pentecostals are really speaking some sort of heavenly, angelic language.
The second theory about tongues I'm familiar with is the idea that 'tongues' is simply speaking in other languages. This is clearly what happened on the day of Pentecost, when the apostles began speaking tongues to a large crowd. There are also reports of miracles in which men or women say or hear something in one language, only to later learn that someone heard a different language, often one the speaker doesn't know. So I certainly believe that this is a possible explanation of tongues. I'm not sure whether the Holy Spirit's intervention in this case affects the speaker or the listener. Does the speaker speak in some sort of magical language that is understood by anyone who hears it as his own tongue? Or, does the speaker talk 'plainly' in his own language, and at some point the sound magically translates for the listener's ear? I guess it's a subtle difference, but one I think about.
Another theory that I recently came into was an idea that a speaker of tongues spoke in the common language, but spoke in riddles like an oracle. Just think about the famous Croesus oracle, in which the priestess warned that the Lydian King that "if you cross the river, a great empire will be destroyed." He assumed she meant the Persians, whom he planned to attack, would be destroyed, but it was his own kingdom that was eradicated in the battle. Since a fair amount of this section of 1 Corinthians emphasizes the need for clarity and speaking plainly, it makes me wonder if Paul's concern was not people speaking in foreign languages, but simply not speaking in a way that was accessible to the common people. (It's important to remember, I think, that early Christians were often slaves and poor people. Good educations weren't necessarily in their reach.)
Thinking about all this made me wonder what Paul would have thought of the Catholic practice of delivering the Mass in Latin long after Latin ceased to be the common tongue. As the priests of the Middle Ages recited scripture, their audiences had no idea what was being said and had to trust the interpretation of church leaders. Latin may have been the tongue of the Church, and priests therefore would have been speaking in a holy tongue, but fat lot of good it did for the average peasant!