Adam Delehanty, who keeps our schedules straight at WQXR, just asked, "This may be a naïve question, but why does Mozart's music all have "K." numbers after it?" It's a great question.
A lot of composers' music is listed by opus number (abbreviated Op.), but back in the 19th century, a musicologist named Köchel (Ludwig Alois Ferdinand Ritter von Köchel, to be exact) did the world a huge favor by cataloguing all of Mozart's music. So Mozart's compositions have “K. for Köchel” numbers.
Adam then asked if Mozart was the only composer with "K." numbers, and I said no, the great 20th century harpsichordist Ralph Kirkpatrick catalogued Domenico Scarlatti's music, so it has "K. for Kirkpatrick" numbers. Otto Erich Deutsch put Franz Schubert's music in order, so Schubert gets "D." numbers. And Johann Sebastian Bach's music has three letters: BWV, for Bach-Werke-Verzeichnis, which is German for "Bach Works Catalogue." Amazingly enough, the BWV numbers have only been around since 1950.
I think my favorite catalogue letters are "Hob.," short for Hoboken-Verzeichnis. Not because Haydn spent time in the New Jersey city where Frank Sinatra was born -- Anthony van Hoboken was a Dutchman who did for Haydn what Köchel did for Mozart.
And I also have a soft spot for "WoO" (woo!), short for Werke ohne Opuszahl (in English, "works without Opus number"). As the name suggests, those got assigned ex post facto to bits and pieces that Beethoven didn't give an opus number to.