This is considered to be within modern Roman Catholic theology and practice, but is not very common (i.e. Its easy to go to mass every Sunday your entire life and never see an example of it), is not traditional, and is viewed with skepticism by many lay people who are aware of it. Also, it is not allowed to get as out of hand as in some charismatic denominations- the most questionable extremes from the charismatic movement in general are usually absent from the Roman Catholic version thereof.
I can remember as a preteen or a young teen being roped into a spirtual retreat where they had some sort of a charismatic event one night. I had no idea it would be happening, and probably had no idea what a charismatic was, though they did provide some sort of an introduction to explain what would be happening the night itself. People were babbling nonsense words and laughing and crying uncontrollably in non-ironic ways. Some people collapsed to the ground or ran around. I think others may have claimed to have been seeing visions. Some folks were shouting. I was frankly horrified and just stood there stone faced. People couldn't believe I couldn't "feel the spirit". My impression at the time was that it seemed like a combination of mass delusion, some young people happy to have found a religious excuse to act like crazy people, and some people faking it to go along with the expectations of others. Also, it was extremely crowded, noisy, and choatic. I was not impressed. And it was a divide between me and the others there for the rest of the weekend- I don't think we had any real arguments over it but some people insisted I must have felt some spirit I didn't feel or have seen some things that I didn't see, and I just told them that I didn't feel or see anything apart from the ways people were "reacting".
As an adult, I do know one Roman Catholic who claims to be able to speak in tongues, but who will only say so if asked directly.
I will simply say that it is on a long list of things I have no interest in ever seeing again and pretty much leave it at that. If people get something out of this, provided that they at no point attack or restrain people to "cast out demons" the way some charismatic Protestants have occasionally done, I guess its okay to start babbling in pretend languages and randomly laughing and crying. Who am I to judge?
Maybe there is even something to it (Though I doubt it, except in so far as I could I suppose see how praying without real words would be a way of tapping into the universal spirit and feeling the oneness of all things and God in a way others might feel through more traditional prayer and meditation and sacraments. I don't think that's what charismatics claim they are doing, but maybe its a positive thing that happens even if they think its something else they are doing. It clears their minds for more profound spiritual experience. It also could be cathartic for some people, I suppose.).
So, basically, I am not a fan, but I am not going to condemn it either in its less extreme forms. People can go do their thing and I'll make sure not to be in those places at those times and everything will be fine.