My current favorite is The "Little" Fugue in G Minor, BWV 578. ("A fugue is a contrapuntal piece of music wherein a particular melody is played in a number of voices, each voice introduced in turn by playing the melody." wiktionary)
To get a feeling for how The Little Fugue introduces the melody over and over, in multiple voices, each continuing to play over the others and yet still sound "good", check out this "piano-roll" animated rendition of this piece on youtube.
The above piece is performed on a piano-like instrument with a pedals, so the pianist can play a bass melody with his feet, just like an organist. And I think you would need that with this piece. I'm not sure how someone would like all the parts with just two hands.
Now the more fun performances are these...
The Canadian Brass:
The Swingle Singers:
Leopold Stokowski's orchestral arrangement:
You can search for other renditions of this fugue on other instruments. Wendy Carlos did a recording using a Moog synthesizer in Switched-On-Bach Boxed Set. The original instrument was of course, organ.
Bach's most famous organ piece is The Toccata and Fugue in D Minor, BWV 565 which may not have been written by Bach (!) and may have originally been a violin piece (!!). See the wikipedia article here. And here's what the violin piece might have originally sounded like:
I rather like Don Dorsey's synthesized version of The Toccata and Fugue in Bach Busters.
No youtube version of Don Dorsey's version. But there is this guitar performance:
My other favorites include the Brandenburg concertos, The Passacaglia and Fugue in C Minor (which is another piece arranged by Leopold Stokowski for orchestra)...
...and several pieces from the Anna Magdalena notebook.
I'm not a fan of Bach's vocal music.
I own a "complete" collection of Bach's music (153 CDs, excluding his religious vocal music), including several recordings of my favorite pieces.