Heh, yeah, alvaro's code is the way to go if your boxes are axis-aligned. The algorithm I presented will work for any arbitrary box, but is overkill if your boxes never rotate. And looking at his, I realized that I didn't include the tests for if a point is inside the box, return 0 distance. As it stands, the code I presented will give the distance to the box's wireframe, so points inside the box will have a non-0 distance value. On an arbitrary box (as long as it is a box, and not a rhombus or trapezoid or other funny shape) you can test this easily by checking the values for u of the A->B and A->C tests, and if both do not require clamping (ie, both are in the range of [0,1]) then the point is inside the box, and you can return 0 for the distance.

Heh, yeah, alvaro's code is the way to go if your boxes are axis-aligned. The algorithm I presented will work for any arbitrary box, but is overkill if your boxes never rotate.