The following comments are from an interview with Baroque specialist Ton Koopman, in which he discusses the use of the fermata in Bach's chorales. This is of particular interest to church musicians or congregational singers who want to know what to do with the fermata in hymns of German origin.
"Take the issue of how to perform fermatas in the chorales - should the note under the fermata be held longer? For a long time the conventional view was not to hold these notes; and then Harnoncourt started to extend them. For years, everybody followed him in not extending the fermatas, and then he reverted to the previous practice. And now everybody is following him again! Nobody is thinking why it's being done. So with these things, I do my own research, and I'm very independent. In the case of the fermatas, I think the earlier practice is the right one - they should not be held. I see no reason to do that. David Schildkret wrote an article about this in the Riemenschneider Bach journal in 1989; after examining many chorale books, he concluded quite clearly that the fermata is just an indication of the transition from one line of the chorale to the next. There's also another indication that you should not slow down at a fermata - and you should be an organist to know that: in the Orgelbüchlein, there are lots of fermatas at the end of individual lines of the chorale melody, but there are semiquavers still going on in one of the other parts. You can see something similar in some of the early cantatas - the part with the chorale has a fermata, while at the same time the violin obbligato part is still going on, without a pause. So I think nobody can honestly maintain, after having done research, that you should keep the fermatas. Yes, the fermata does mark a cadenza in some arias. But if you want to make cadenzas at those points in the chorales, you should recall that there's one text about Bach's organ playing, where one of his students - I don't remember who it is, I think it was Agricola but I'm not certain - said that Bach didn't like organists who introduced runs and ornaments at the end of chorale lines. So you have corroborating evidence, from several sides, proving that you should not hold fermatas in chorales."