Speaking specifically about a mayor, you are often going to get a different perspective from the mayor than you will a character of lower status.  Since The Hunger Games has already been mentioned, let’s talk about the mayor in District 12.  Katniss is a member of the Seam, where the lower class lives.  She is very poor, and knows nothing of what is going on in other districts or the Capital.  She has no idea, for example, that there is a rebellion beginning.  Yet when she visits the mayor’s house and sees the rebellion on his secret TV, we see the mayor looking worried.  It is in first person, as others have mentioned, but we get a glimpse of what the mayor is thinking from Katniss’s interpretation of the look on this face.  This is knowledge that not many have.

I agree--Holden Caullfield was a great example of first person perspective in The Catcher in the Rye.  His narration of the story was like living in his head, which made for some pretty humorous moments and some equally tragic ones. 

A really recent popular novel to be written in first person narrative perspective is The Hunger Games.  Using Katniss' first person perspective really drops the reader straight into the middle of the action, which I think is one reason why my students enjoyed it so much. 

I am going to intepret this post as asking how a character's thoughts help to define him/her in a work of fiction. 

The most common way for an author to provide access to a character's thoughts is to use "direct narration" or first person narrative perspective. When using first person point of view, a writer creates a character through his/her internal dialogue. This often includes feelings but in many cases focuses on a character's thoughts. 

Some examples of well-known characters developed with first person perspective might include Holden Caulfield from Catcher in the Rye. 

Posing the question "What are some other examples of memorable characters developed through the first person narrative perspective?" we're bound to get some good answers...