Cognitive Dissonance

One of the more pertinent cognitive theories to belief and how a "believer" responds to a evidence against the belief:

From wikipedia: (Full entry here)

Cognitive dissonance is a psychological state that describes the uncomfortable feeling between what one holds to be true and what one knows to be true. Similar to ambivalence, the term cognitive dissonance describes conflicting thoughts or beliefs (cognitions) that occur at the same time, or when engaged in behaviors that conflict with one's beliefs. In academic literature, the term refers to attempts to reduce the discomfort of conflicting thoughts, by performing actions that are opposite to one's beliefs.

In simple terms, it can be the filtering of information that conflicts with what one already believes, in an effort to ignore that information and reinforce one's beliefs. In detailed terms, it is the perception of incompatibility between two cognitions, where "cognition" is defined as any element of knowledge, including attitude, emotion, belief, or behavior. The theory of cognitive dissonance states that contradicting cognitions serve as a driving force that compels the mind to acquire or invent new thoughts or beliefs, or to modify existing beliefs, so as to reduce the amount of dissonance (conflict) between cognitions. Experiments have attempted to quantify this hypothetical drive. Some of these have examined how beliefs often change to match behavior when beliefs and behavior are in conflict.

An additional entry in the wiki entry makes interesting reading from a religious incident causing cognitive dissonance:

The Great Disappointment of 1844: "...believers experienced tension following the failure of Jesus' reappearance in 1844 which led to a variety of new explanations. The various solutions form a part of the teachings of the different groups that outlived the disappointment."