I disregard original image ratio when cropping. When I crop I give more consideration to 5:4 and 1:1 but I don't use these exclusively. I prefer aspect ratios with small denominators in its simplest rational form.
I suppose you mean odd aspect ratio. It can be odd to you but it seems natural to me. See http://www.cl.cam.ac.uk/~mgk25/iso-paper.html for details.
As a fellow forum member has already pointed the golden ratio, golden mean, etc... as defined in mathematical writings is (1+√5)/2 and it's denoted by Φ (Greek letter phi). Φ is an irrational number, it's the limit of the ratio of successive terms in the Fibonacci sequence and has other interesting properties (As does 0, 1, π, e, etc...). Why to call the different number 1.5 the golden ratio againsting the established notation?. It's pointless in my opinion, it's analogue to referring to 6 as π (Greek letter pi), that just generates confusion.
I agree that 3:2 usually gives a pleasing composition, it's a good thumb rule, like the rule of thirds but art is not about following thumb rules. Some artists may like the 3:2 aspect ratios it so much that they use it exclusively or almost, like grayscale photography, infrared photography, sports photography, photographic portraits, landscape photography, baroque music, classical era music, romantic era music, jazz, etc... but anyhow that don't makes any of them special in its category (Photography or music in these examples) for the rest of us. I disagree that there is anything artistically special about the 3:2 aspect ratio or Φ:1 for that matter. That's my opinion.
On the technical side, aspect ratios which are ratios of small positive integers are nice in that they allow more granularity when choosing sizes when its dimension is quantized (For instance, sizes of images). In this regard, 3:2 (1.5) is preferred to 205:137 (1.496) even if artistically there is little difference. For instance, JPEG images with no chroma subsampling without internal padding are limited to sizes multiples of (24, 16) and (3280, 2192) respectively for 3:2 and 205:137 aspect ratios.