"Air on the G String - Orchestral Suite No. 3, Movement 2, BWV 1068" (J.S. Bach)

I first heard the piece known as "Air on the G String" (a nickname given to the second movement of J.S. Bach's Orchestral Suite No. 3 after 19th century German violinist August Wilhelmj transposed it from D major to C major, thereby allowing one to play the melody completely on the G string of a violin) when I was a little kid.

My mom, ever the audiophile and music fan, had a copy of the avant-garde album Switched on Bach (1968) by electronic music artist Wendy Carlos.  If you're not familiar with the album, it's understandable; it has been out of print for a number of years, unfortunately.  On it, Carlos uses the Moog synthesizer to recreate a number of Bach's "greatest hits" with some pretty dramatic results.  Most importantly, it's futuristic while still respecting the source material, which keeps it from being just some experimental novelty record.

The second track of Switched on Bach is "Air on the G String," and it became a fast favorite of mine as a kid.  Carlos's arrangement for the synthesizer and the stereo separation of the recording push Bach's melody to the forefront, showcasing just what a beautiful melody it is.

I didn't hear "Air on the G String" performed by actual strings, though, until I was a pre-teen.  I was up early one Saturday morning, long before everyone else, and I started channel surfing to see what was on at that time of day.  I ended up landing on either A&E or Bravo (back when they had actual arts programming instead of dreck), and there was a string quintet on an empty stage, playing the piece.  It was only some interstitial clip that the station was using to fill time until the next scheduled program, but it was so achingly beautiful that I watched the whole thing.  

Listening to the piece as the sun came up and beamed through our living room windows, I couldn't help but get a little choked up.  The string version has been my favorite ever since.

Anyway, it's moments and memories like that that made me want to create this list.

"Jesu, Joy of Man's Desiring" (J.S. Bach)

"Jesu, Joy of Man's Desiring."  A.K.A. "Chorale from Cantata 147."
However you wish to refer to it, I fell in love with this piece of music as a kid.  

Asheville, NC's ABC affiliate, WLOS-TV, used it in station identification spots during the holiday season for much of the early 80s.  I remember, the first time I heard it, it stopped me in my tracks (I probably was shuffling across the living room carpet in sock feet, trying to build up a static charge to shock my dad—a favorite pastime of mine in the winter).  It was quite possibly the most joyous, beautiful piece of music I'd ever heard.  
Although Bach composed it as a chorale (and I've sung it as such many times), I actually prefer it the way I first experienced it: as an instrumental.  
When it's played correctly, that is.
By that, I mean conductors and performers tend to have two tendencies when performing this piece of music: a) they drag the tempo so much that it sinks under its own weight, or b) they take it at such a breakneck pace that the notes completely blur.  Really, the song should take about 3:45 - 4:00 to perform.  Not 7:00.  Not 2:00.
Also, this composition (like many others of his) is a dance.  And as with any dance, it's meant to have a little bounce to it when performed.  You should be able to not only hear but also feel the basso continuo in every Bach song—especially this one.
Anyway, nearly 30 years after I first heard this piece, I'd venture to say it is still my favorite J.S. Bach composition—maybe even my favorite classical composition—of all time.

"Brandenburg Concerto #3 in G mjr, 1-3" (J.S. Bach)

J.S. Bach is my favorite classical composer, hands down.  
Beethoven runs a close second in terms of melodies that grab me.
And then I have other faves (Gabriel Fauré, Erik Satie, Claude Debussy, Antonio Vivaldi, Giacomo Puccini, Franz Liszt, George Gershwin, to name a few.)
But inevitably people will say, "Well, Mozart, too.  Right?" 
Mozart, though brilliant, always was a little too cute and clever for his own damn good; I just hear a bratty kid every time I listen to his music, and it makes me want to turn it off.  (I have a similar reaction to Picasso's paintings.  Although I find his works intriguing, he was a total asshole--especially to women, and it leaves me feeling cold about his work.)
Anyway, growing up in the Lutheran church, I heard a lot of Bach--what with Bach having been a Lutheran himself.  Luckily, I really liked the music.  Even as a young kid, when someone asked me what music I enjoyed, along with rattling off a slew of mid-80s performers (some of which had staying power, others...not so much), I'd inevitably mention Bach, usually to the person's surprise.  I think adults just assumed it was something my parents had trained me to say, and kids my age just figured it was me being pretentious.  
But I really did like Bach.
A lot of it probably had to do with the album Switched-on Bach, which my mom often would play while doing housework.  For the uninitiated, Switched-on Bach is a (sadly) out-of-print 1968 album by Wendy Carlos (an interesting and talented figure herself, who is worth reading about) that uses Moog synthesizers to recreate some of Bach's "greatest hits" with pretty stunning, timeless results.  The album not only held the distinction of being one of the best-selling classical albums of all time, but it also introduced the Moog synth as a real instrument, not just a novelty that could be used for generating sound effects and gray noise.
For me, being a kid of the funky late 70s and New Wave-y early 80s, the album fit easily into the sonic palette that Stevie Wonder used on his "classic period" of albums as well as bands like Devo and Gary Numan & Tubeway Army.  (But I'm sure, in 1968, the album probably sounded like it had come from the year 2068.)  
But I can't owe my affection for Bach completely to Wendy Carlos and her futuristic synths.   It's Bach's singular approach to melody, counterpoint, and rhythm that have always engaged me.  His music requires equal amounts of precision and heart to perform well.  If you're missing one element or the other, what you get is the sound of Bach sluggishly rotating in his grave.
This is very true of "Brandenburg Concerto #3 in G major."  While I enjoy all six parts of this Baroque masterpiece, #3 always grabbed me the most.
The first movement (Adagio) has this bright, sunny feel that chugs along with this unceasing momentum.  There's also astounding counterpoint and all sorts of subtle interplay among the violas, violins, and cellos, where one set of instruments will start a line and then hand it off to the next set of instruments.
Then there's Movement 2.  Which kind of isn't a "movement" at all.  
The sheet music is just two chords on a single measure.  That's it.  Music historians sometimes argue about Bach's intent, but I think it's pretty obvious that he expected someone (lead violinist, maybe the harpsichordist) to improvise a solo.  How badass is that?  It's basically jazz circa 1721.  (Side note: I realize that this type of soloing is a Baroque technique that was not necessarily limited to Bach.  But I still think it's pretty gutsy to have two movements separated by a piece where you "give the drummer some.")
Finally, Movement 3 (Allegro) takes off like a racehorse, and it doesn't let up until the final note.  Once again, Bach uses the technique of one instrument/set of instruments starting a line and then handing it off to the next instrument, with the lead violin soloing every few measures before disappearing back into the swirling rush of notes.
There's also the basso continuo ("continuous bassline") throughout, played by the double bass and harpsichord.  I believe it's this specific Baroque technique and Bach's mastery of it that make me love this music.  It's that unceasing, melodic bass that gives Bach's music--and this composition in particular--a certain bounce that feels almost indebted to folk rhythms.  It's earthy yet spiritual music, and you can't get any better than that.
(P.S. I really like this rendition I found online performed by EUBO--the European Baroque Orchestra--from 2011.  It's a group that auditions and selects completely new members every year.)