The tricky part is to define what is the volume of a biomolecule as it is a folded chain full of bumps and holes. Water is all around and in the folded structure and is actually important to keep the conformation of at least some of the proteins/RNA/DNA.
At the same time we know that 60% of your body in mass is water. Let's visualize that. Bio molecules have roughly the same weight per volume than water. Now add into the equation that a good third of the filled actually is water due to the structure holes, adsorption etc. You now have roughly:
% empty space = 60%-(40%/3)= 47%
To help think about it imagine a grid with roughly one cell out of two being filled. That looks pretty crowded to me. Then you of course have variations with blood and secretions on one side and bones on the other but you have the big picture.
For an example look at an electron microscopy picture of a striated muscle cell: http://histology.med.umich.edu/sites/default/files/muscleQ4.jpg. It looks pretty much like the half filled grid isn't it? Of course seeing individual molecules is hard but the white space correspond to mostly empty space with a couple of actine fibers. The dark corresponds to actine+myosine fibers: an extremely tight space. And we have roughly half of each :-)