What is the Catholic view on speaking in tongues?
St. Paul is the one who spelled it out for us, most notably in 1 Corinthians 12 and 14. Essentially it's a real phenomenon and a way the Holy Spirit can speak through people, though there are many other gifts to ask for that are far more important.
The principle "Ask (insistently and with faith) and you will receive" applies here, as it does in most things in the spiritual life. So it's no surprise that these extraordinary gifts flower today most commonly in the communities where they are sought most ardently: the charismatic communities, both Catholic and Protestant.
That said, the extraordinary and impressive nature of tongues and gifts like them can easily trigger the less edifying elements of the human psyche, so psychological suggestion and outright fraud can give rise to things that look like the Spirit's action but aren't.
Still, the genuine article is found more often than you might think. There are many ways in we "hear what the Spirit says to the churches" (Revelation 2:7): this isn't the primary one (Church teaching through Spirit-guided Magisterium is) but it's a very real one. It's messy and hard to manage (the Spirit's action always is) and it's only ever at the service of charity and it's not for everyone, but it's real. Check this out if you want to go (a lot) deeper.
God bless you!
- Father Shane