One of our fellow-Twitterers asked about what's a good set of pieces to start listening to Bach's music. We thought about it, and decided that there was no earthly way of answering the question in a 140-character tweet.
Actually, Bach wrote so much in so many styles that the answer very much depends on where you're coming from. In particular, if you're a devout Christian, you start at a very different place than if you're not. To start with, here's a selection of my more secular favourites:
Top of my list, albeit not for the faint-hearted, is the Violin Partita no. 2 in D minor, BWV 1004, with its awesome last movement Chaconne. Although there's just the one instrument playing, it demands complete concentration, and you feel at the end as if you've just come out of an emotional wringer, but in a deeply satisfying way. Here's a Youtube video of the legendary Jascha Heifetz performing the work.
The Chaconne has been arranged for just about every instrument on the planet, with excellent versions for guitar (by Julian Bream and several others) and piano (by Ferrucio Busoni).
If you're in a darker, more contemplative mood, start with the Suite no. 1 for solo cello in G Major, BWV 1007. If you're not up to 30 minutes of solo violin or cello, however, much of the solo piano music is a bit easier to get to grips with. This is particularly so when played by the late Canadian pianist Glenn Gould, who played a large quantity of it in a quite inimitable style, bringing the music to life with masses of vitality and immediacy. Gould made no concessions to period-instrument purists, and he's so off-centre that he offends many real baroque afficionados, but it works for me and I love every minute of his playing. Start with the French Suites, BWV 812-817, or the F sharp minor Toccata, BWV 910 from Gould's Toccatas and Inventions album.
Gould is also one of several good interpreters of the Piano Concertos - I'm very fond of Piano Concerto no. 1, BWV 1052. Here's a Youtube clip of Gould and Bernstein:
If you prefer more baroque, upbeat music of the sort that you imagine in a 17th century court event, the Double violin concerto, BWV 1043 is lovely. The six Brandenburg concertos are very well loved: personally, I find them a bit patchy but no. 3 is a favourite: upbeat and textured.