The Church through out Her 2,000 year history has always recognized
the various gifts of the Holy Spirit including tongues.
In the early centuries, there was a movement called Montanism which
eventually went into heresy. It over emphasized personal prophecy
and tongues to the exclusion of Scripture and Sacred Tradition. In
effect, it was like a Charismatic Gnosticism. By the Middle Ages, the Church really stopped talking or teaching
about the more phenomenal gifts such as tongues.
That said, the Church has always had folks who operated with these gifts. In particular,
the Church's history is rife with people to whom God gave the gift
The important thing to remember is that Tongues, like any other
gift, is a grace or a gift.
It operates ex-officio, it has nothing
to do with holiness.
Tongues is simply a prayer of the Spirit. It is a mystery, like many other
matters of faith.
P.S. You can add this Scripture passage to Mike's list:
2 For he that speaketh in an unknown tongue speaketh not unto men, but unto God: for no man understands him; howbeit in the spirit he speaketh mysteries.
1 Corinthians 14:2