What are the neurobiological factors associated with intelligence in animals? For example, is there a well-defined relationship between "number of neurons in the cortex" and some measure of "intelligence" in animals?

I'm familiar with the encephalization quotient - that is, "the ratio between actual brain mass and predicted brain mass for an animal of a given size," which is hypothesized to be a rough estimate of an animal's intelligence.  Are there any other similar concepts?  Or, are there any brain structures or measures of complexity that are only present in "higher functioning" animals?
Title question: See below
Question 1: Sort of.
Question 2: Yes.
Question 3: Yes. 


The wrinkly outer layer of the human brain, the neocortex, is an anatomical feature found only in mammals. It is largely responsible for our ability to process sensory information in great detail, and plays a large role in memory formation, recognition, and higher thought. 

Unlike the thalamus or cerebellum, the shapes of which could be characterized as 'lumps', the neocortex can be thought of as a sheet; a larger surface area is related a larger neocortex, which translates directly to a greater supply of computational resources. Thus the wrinkly nature of the exterior of the human brain shows its usefulness; more wrinkles means more surface area.

It may be useful to keep in mind with regard to humans that our own accomplishments, often attributed to our intelligence (and rightly so), have depended on much more than our brain. Our physical ability to speak, which allows us to quickly share ideas and learn from one another, is not a feature shared with other animals (See reference 1). Moreover, our ability to manipulate objects allows us to record information, enabling us to much more easily stand on the shoulders of the giants who have preceded us. Were we lacking in either of these abilities, or both, we may not appear as intelligent as we do.

Diagrams:


Here is a diagram of the brains of various animals including both mammals and non-mammals: http://www.neurocomputing.org/Images/Brain_Introduction/Comparative_Neuro/brainpicts.gif
Unfortunately, I'm new and don't have the reputation score sufficient to post more than two links


Notes for further reading: 


Jeff Hawkins' book "On Intelligence"
Although more perception-specific, the topic of cortical magnification is a handy topic to know


References: 


http://www.mpi.nl/q-a/questions-and-answers/why-cant-apes-speak
On Intelligence, by Jeff Hawkins