Is there a school of thought or concept that acknowledges that people aren't rational actors when it comes to economic decisions? People are subject to all sorts of cognitive biases.

For example:


Advertising works, and not just by making people aware of a product,
but by appealing to emotional quirks. 

People are subject to psychological pricing.


It seems clear that people aren't entirely cold calculating rational agents, calculating the maximum utility and acting accordingly. 

Is this acknowledged in any economic theories, or is it more or less ignored?
Yes this is a blossoming area of research in economics and it spans approaches from psychology to game theory, social theory, and cultural biases.

A lot of these approaches fall under the rubric of "Behavioral Economics".  Unlike classical market economics which often begins with assumptions around individual and collective rationality, behavioral economics seeks to study how economic decisions are actually made by individuals and groups (i.e. it does not take utility-maximizing rationality as an assumption but instead studies its role in animating economic decisions and systems).

"Irrational" behavior should not be confused with unexplainable or unpredictable behavior.  A simple example is why people buy lottery tickets.  This may be irrational under classical utility theory, but it is explainable and can be modeled, tested, and incorporated into larger economic frameworks like market options pricing by using behavioral economics.