Yeah, as Michael mentioned, I do lots of squares.  Really, it's just the way I see.  Something about the rule of thirds within a square really appeals to me.  And on rare occasions when an image works with dead-centered composition, square can really pack a punch.  When I used to shoot 35mm, I found myself constantly wanting to chop off one end or the other, so I just went with it and bought a 6x6.
A lot of times for me, since I primarily photograph people, it's about negative space (no pun intended.)  I like room for context, whether it's explicit or implicit.  I use my 6x6 mostly for candids, so there really is no time to think about anything other than 'the moment' before I hit the shutter.  Sometimes I find the need to crop something out.  Usually, though, I've managed to take it all in subconsciously (I know that sounds snobby) so I can generally print full frame.
Dead Link Removed
 - CJ