Re: What is your favorite piece of Classical music?
Not strictly speaking the specific genre of the Classical Era (1750-1820) but rather the general Common Practice period which is really anytime from the Renaissance up to the early 20th century.
Just out of curiosity... why do you limit it so,
Jockboy? I'm getting into an early music phase, and some things by Ockegham, Tallis, and Byrd would have to go on my list.
Well, I think there's a particular thing called "Classical Music" which, granted, is still done today, but it's no longer the "popular music" of the culture. Yes, Franz Liszt was the first rock star; no, he wouldn't be a rock star today (unless he did rock music).
I think it's fair to say that so-called "classical music" was never popular music, especially before the French Revolution. When 95% of the population are rural peasants who've never seen the inside of a concert hall, I think that folk music would have to be counted as the most popular music of the day. That changed later on, of course, especially in the latter half of the nineteenth century, but I'm not sure classical music ever achieved the popularity of folk songs, marching bands, and so on.
I appreciate the analysis in your post,
Críostóir. One other thing I'd add regarding the difference between classical and popular music is that (I don't quite know how to say this) their diversity is different. Popular music is mostly melodically and timbrely diverse -- that is to say, most of its appeal comes from the catchiness of the tune and the uniqueness of the instrumentation. Classical music tends to be more diverse in terms of harmony and rhythm. Popular music rarely goes beyond basic tonal harmony (the Beach Boys, of all people, are a notable exception) and rhythmically, despite widespread belief, it is quite four-square (when's the last time you heard a pop song in 9/8 or 5/4 time?).
As for my favorites -- it changes every couple of weeks or so.

I like my harmony a bit more spicy than most, so I am a pretty big fan of 20th century music. Anyway, for now, in no particular order:
Walton, Symphony 1
Barber, Cello Concerto
Milhoud, Le Boeuf sur le Toit
Bartok, Piano Concerto 1
Roy Harris, Symphony 3
Sibelius, Symphony 3
I've also got a soft spot for the Russians:
Rimsky-Korsakov, Sheherazade, Russian Easter Overture
Borodin, Symphony 2
Balakirev, Symphonies 1 & 2
Shostakovich, Symphonies 4, 13 & 15, Cello Concerto 1
Miaskovsky, Symphony 6
Prokofiev, Piano Concerto 3
Rachmaninoff, Symphonic Dances