What is happening to Suzanne's eyes during this use of the Boolean modifier? So, I used a Boolean modifier on Suzanne and a fairly default cylinder. The results, as they move along, go something like this:  video.  

The modifier is set to union.  As you can see, something strange is happening: only her eyes appear.  I did do some interesting things with it previously using the subsurface modifier - but that time, her eyes dissapeared, as opposed to the rest of her head!

Kudos to anyone who can help me with this.
You are using a non manifold mesh. Basicly, non manifold means, in layman's terms, not water tight. 

Here is an example:



The cube has a hole in it. In Suzanne's case, its the fact that her eyes aren't attached to her head.

Here is a quick way to fix Suzanne:



Note: I use the loop tools add-on accessed by W