Controller classes in Entity API
No.

'controller class' => 'ExampleTaskController',


  controller class: The name of the class that is used to load the
  objects. The class has to implement the
  DrupalEntityControllerInterface interface. Leave blank to use the
  DrupalDefaultEntityController implementation.


Says nothing about where the class code actually lives in Drupal. The easiest place to put it is in the same file your declaring hook_entity_info. Because since it's in the same file it will be found by PHP because the class will have the same file scope as your hook_entity_info implementation, and likely the other hook functions needed for your entity.

In PHP there are only 3 scopes: file scope, function scope and global scope.

So how can it live outside of say YOURMODULE.module. You declare where this class can be found in your YOURMODULE.info file with the files[] directive.

Such as:

name = my custom module
package = other
files[]= EntityClassController.inc


Files defined by the files[] entries are scanned for class definitions and included automatically by Drupal in its bootstrap phase to be available as-needed by running code. So your class would live in the file location of DRUPAL_ROOT\sites\all\modules\mymodule\EntityConroller.inc as an example.

Alot of times to organize code better developers add subfolders, or submodules to their modules you could for instance declare the class to live in an includes folder in your modules folder with:

files[]= includes/ExampleTaskContoller.inc


Some hook functions such as hook_views_api and hook_menu allow you to define a file location where the page callback function can be found (in the case of hook_menu) or where your views implementation classes/handlers/etc may be found in the case of views.

For instance hook_menu allows for the following 2 keys to better organize where page callback functions live in your source code:


  "file": A file that will be included before the page callback is
  called; this allows page callback functions to be in separate files.
  The file should be relative to the implementing module's directory
  unless otherwise specified by the "file path" option. Does not apply
  to other callbacks (only page callback).
  
  "file path": The path to the directory containing the file specified
  in "file". This defaults to the path to the module implementing the
  hook.


Views allows 1 to define where views includes lives via hook_views_api:


  path: (optional) If includes are stored somewhere other than within
  the root module directory, specify its path here.
  
  template path: (optional) A path where the module has stored it's
  views template files. When you have specificed this key views
  automatically uses the template files for the views. You can use the
  same naming conventions like for normal views template files.