Yehuda, your third solution is very useful! I like both of yours, though, and I believe that I'll have uses for both of them. I appreciate all of your work. However, I'm curious; I'm noticing this and I want to know what you think about it:

Whenever I have all 3 of those planes showing simultaneously, it seems that parts of the graph are "cut off" as you can see by the two images above. The problem doesn't exist whenever I select any combination of only two planes; only when all three are selected. Changing the opacity down all the way to zero still gives the same problem. Do you have any idea what's causing this?

Of course you can do that, but it will just clutter your graphics one simple example of doing that is given below to show how it can be done and how the clutter looks like. Notice that I didn't make any effort to optimize anything, nor to make it general. best yehuda

Module[{xticks, yticks, zticks, xends, yends, zends},
 xticks = yticks = zticks = Range[-1, 1, 0.5];
 xends = yends = zends = {-1, 1};
 Show[ParametricPlot3D[{{x, Im[I^(5 x)], Re[I^(5 x)]}}, {x, -1, 1}, 
   AxesLabel -> {"Real x", "Imaginary y", "Real y"}, PlotRange -> All,
    PlotStyle -> {Thick, Red}], 
  Graphics3D[
   Flatten@{Blue, 
     Map[Line, Outer[{#3, #1, #2} &, yticks, zticks, xends], {2}], 
     Map[Line, Outer[{#1, #3, #2} &, xticks, zticks, yends], {2}],
     Map[Line, Outer[{##} &, xticks, yticks, zends], {2}]}], 
  ImageSize -> 500]]

Thanks, that helps greatly. Is there a way that I can choose the intervals for those?

Also, although the face grids are useful, is there a way to actually create a grid that actually goes through the box? Like this (just with fewer grid lines):