Question: What percentage of a unit cell is empty space?

Answer:  It depends on the unit cell, and on the compound within the unit cell.

For metals, where all of the particles are the same size, different types of unit cells have different percentages of empty space.  For example, close-packed structures (such as hexagonally close-packed or cubic close-packed) are approximately 26% empty, while body-centered cubic (bcc) structures are about 32% empty.

For ionic compounds, there's not really a good answer to this question, as every compound will have a different amount of empty space due to the differences in ratios between the cationic and anionic radii.  Common structures which are frequently seen in ionic compounds are the rock-salt structure (which is basically a face-centered cubic structure with the sodium ions in the octahedral holes), the cesium chloride structure, the sphalerite structure (ZnS), the fluorite and antifluorite structures, the wurtzite structure, the nickel arsenide structure, and the perovskite structure.  Even for compounds with the same basic structure, the amount of empty space will differ due to the differences in ionic radii.

One way you can determine the structure of an ionic compound is to study the radius ratio, which is a ratio of the cation radius to that of the anion.  The smaller the radius ratio, the smaller the coordination number of the compound.

For more information about unit cells, have a look at the excellent textbook Inorganic Chemistry, by Shriver, Atkins, and Langford.  This book is easy to read and has more info than you can shake a stick at.  If you're merely curious, it can probably be found at any university library.  If you're serious about learning inorganic chemistry, the ISBN is 0-7167-2079-5.  Look for it at amazon.com.