I usually prefer complete depth of field when possible simply because I feel that if a subject is worth photographing, and by extension worth looking at, we should be able to see it sharply. That also goes for the environment. However there are exceptions. For bird and wildlife photography, since we have to use long lenses, the backgrounds go out of focus. That is often ideal, actually, because it forces all of the attention on the subject.
With respect to foregrounds going out of focus, I believe this is rarely correct. Only if the foreground is so out of focus that it's a haze of color does it work well. But, in art, there are always exceptions, and I think this picture of a lion in Botswana is one of them. The grasses in front are still somewhat defined, but because the lion is so sharp and he's surrounded by softened grasses, to my eye at least this works.
I took this with film in 2000 using a Mamiay RZ 67 and a 500mm telephoto.