I have been looking for classical music online, and there seems to be some kind of a classification system that I don’t know about. Lots of famous pieces of music seem to have the letters “BWV” or “HWV” appended to the title, followed by a number. BWV 1048, for example, is associated with Bach’s Brandenburg Concerto (type “bwv 1048” into a search engine and it will return the concerto). It seems like there is some kind of a system here. Is there one?
The letters BWV stand for Bach-Werke-Verzeichnis, which is a thematic listing of all of the works of JS Bach. Other composers have had their complete works catalogued in similar ways by musicologists. The Köchel number assigned to each of Mozart’s works is another example.
Cunctator, thanks for the quick and definitive reply. My only question now is, who made the list? Or are his works simply numbered chronologically?
They’re numbering systems; catalogs. Somebody sat down and figured out the chronology of the compositions by Bach and (I think) Handel. The numbering system which has become the standardized chronology, the “official” order of composition for Bach is BWV–Bach-Werke-Verzeichnis, it says here; "Bach Works Catalogue. I assume that Handel’s system is Handel-Werke-Verzeichnis.
Mozart’s compositions, for example, are denoted chronological by a K, for Köchel, the man who devised the catalogue. WFMT, the world’s greatest classical music station, refers to Cosi Fan Tutte, e.g., as "Köchel [pronounced roughly Kershel] 588.
I seem to recall that the BWV system was done by a bloke called Wolfgang Schmieder. It’s a thematic listing, so the BWV numbers are in groups:
1-200 are religious cantatas
232-242 are masses
525-771 are works for organ etc
Try here for some more information.
Like they said, but I’ll add that this is basically the same thing as Opus numbers for other composers. The problem is Bach, Handel and Mozart didn’t number their pieces themselves, so different people could decide differently which piece was Opus 11. The solution was that everybody agreed to use Kochel’s numbering for Mozart’s works, and to be clear they use Kochel numbers [e.g. “K. 142”] instead of Opus [e.g “Opus 11”].
Consequently, numbers from the BWV catalog are also referred to as “Schmieder numbers” and given the prefix “S.” (The numbers are the same: the “Sleepers Awake!” cantata may be listed as either BWV 140 or S. 140.) I once heard a classical DJ identify a Bach composition by its Schmieder number “for all you Schmieder readers out there.”
Schubert’s works were cataloged by Otto Erich Deutsch, so his works all have “D.” numbers (e.g., String Quarter #2 in C, D. 32).
Things get really messy when there is more than one catalog for a composer’s works. Most people use the Ryom Verzeichnis (RV) catalog numbers for Antonio Vivaldi’s works, but there are also competing catalogs from Rinaldi (RC), Pincherle §, Fanna (F), and Rinaldi (RN). Plus standard “opus” numbers. :eek:
…and then there are the Schickele numbers… 
It should be noted that physicist Albert Einstein helped to categorize much of Mozart’s works during his lifetime.
During our music history class, we had to memorize the names of works, and sometimes opus numbers, however, and thankfully, we never had to memorize the numbers made up by the systems we are discussing in this thread.
Look here for a fascinating article about the numbering and editing of Mozart’s works.