I think I speak for a lot of Flux users when I say that the point you really notice is when you're working late at night, and you turn off Flux after your eyes have acclimatised and all of a sudden you feel like you're in a tanning booth.
On the desktop I like it simply because it helps automatically "dim" my display in the evening. I don't use much artificial light in my room [it's basically a mancave after 5:00] so a bright display with the standard color temperature is just an exercise in eye-strain.
I can't be bothered to adjust my brightness, contrast, and temperature manually every evening to avoid eyestrain. Since my monitor doesn't have programmable presets, f.lux definitely provides a great [automatic] solution.
On my iPhone it's actually more of an issue, I find myself disabling it frequently. I think this is mostly because I use my phone in a wide range of "lighting contexts." I might walk from the man-cave to a fluorescent-lit kitchen, and then I'll go out into an incandescent living room.
In my car, I find the low color temperature kind of difficult to read, so I'll usually disable it for road journeys. (It probably doesn't help that I have a dark OS theme and my navigation application has a dark blue "night time" mode that is also time activated.)
Problems: in a lot of dim rooms, the monitor is the main light source, and some webcams have terrible auto white balance. If you're on a Logitech camera it's totally easy, and if you're on a cheap netbook, it's awful. Still, you can solve all that, and we probably will ship a version of this soon.
Granted, I use and like warm lighting at home. I wonder what would be the effect in a house/room that uses daylight lighting.