Between 1783 and 1787 Breitkopf published a collection of four part chorale harmonizations based on Bach's. Most were abstracted from the cantatas; some are from the Passions (St. Matthew, St. John and St. Mark), the Christmas Oratorio and the six motets. The St. Mark Passion and about 100 of the estimated 300 cantatas were lost after the chorale harmonizations were prepared. The chorale harmonizations give the only preserved remainder of these.
The 371 chorale harmonizations were prepared for Breitkopf by Johann Kirnberger and C.P.E. Bach, who finished the collection after Kirnberger died. Breitkopf published 3 or 4 editions. The modern edition, edited by Albert Riemenschneider, corrected many errors after comparison with the original scores as they were abstracted from the cantatas. (A frequent error was accidental substitution of the continuo part for the bass.) The Bach-Riemenschneider edition also contains 69 chorales with figured bass from the Schemelli hymnbook.
Choral performances of most or all of these chorales may be found on YouTube. Just search by the BWV number. If the chorale is contained in a cantata, it is usually in the end, though long cantatas may contain two chorales.
The 371 Chorales Harmonizations may be found in either the Breitkopf collection (out of copyright and freely available at IMSLP) or in the more reliable and well commented Riemenschneider edition.
The JSBChorales website by Margaret Greentree formerly contained MusicXML and other format versions of most of the Chorales. These MusicXML files were the basis of the audio and pdf files here. Since Margaret Greentree's site is no longer available, here is an archive of her files:
I imported Margaret Greentree's files into Musescore and in many cases corrected errors after consulting Riemenschneider's edition of the Chorale Harmonizations. Here are my Musescore 2.x files.
The Bach Cantatas website, maintained by Aryeh Oron contains much vital information.