Also what about aspect ratios? Are we then supposed to be slaves to our cameras' sensor size?
My impression: Yes! The still world seems to be seen through 2:3, just like everything moves in 16:9 nowadays. I really like to re-frame my shots, but I seem to be one of the few people who does that looking around, and I'm always feeling mighty "noobish" doing it.
But talking of cropping: for 2:3->16:9 I usually take two shots, one with more space to one side, because cutting a center-weighted subject to the side of 16:9 ("wallpaper-style") looses a lot of resolution.