Sometimes, but usually just the 'action' mode. For example, I sometimes take pictures of moving trains while I'm on another moving train, and I see the sports mode as a quick way to get a high shutter speed, single-spot focus, etc., without having to set those modes myself. It gives me a half-decent set of default settings, which I can adjust further from there as necessary.
In other words, I see them as a starting point rather than an end point.
That said, my biggest gripe about them with the D7K is that it's very easy to accidentally switch to another mode by hitting the thumbwheel. So I have to watch that.
I don't use the effects or processing modes. I can do that on my computer if I want. (I usually don't.) My wife sometimes uses the fisheye effect on our Canon P&S...it drives me nuts because it's not getting a wider view, just distorting the view you have, and it's not reversible.