I like the work of many classical musicians. Vivaldi and Bach are favorites -- the baroque in general can be listened to in a variety of moods and settings. Henry Purcell lived a short, productive life. His short opera, Dido and Aeneas, is often pleasing even to folks who don't like opera. I like choral religious music such as Allegri's Miserere as well. Classical music, per se, is often associated with the big four -- Haydn, Mozart, Schubert, and Beethoven. It's kinda odd, because if one talks about classical literature or architecture, one is definitely talking about antiquity, but classical music is really early modern era through the Enlightenment and up through the Romantic era. Bruckner and Brahms are excellent. Twentieth century still has some interesting composers, though. I like Gustav Holst, Arvo Part, and John Tavener.
P.S. JR in Pittsburgh, you are a nice fella, but I don't understand despising Mozart unless you are related to Salieri . . .