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.