Where to collect business logic for Entity models? Thinking of entities as an MVC 'Model', where would the business logic for an entity sit? I have a custom EntityController, but that isn't attached to an instance and seems to be intended only for serialization logic. I need a Model class that has the same properties as the entity StdClass, but also has functions for operating on the data and presenting it. 

I am currently wrapping the entity with a real Model class that is created by its static function Model::createFromEntity($entity)
You can use the Entity API which allows to specify the class in hook_entity_info(). Then entity_load() will use that class (assuming that you're using/extending from EntityAPIController, not the core one) then it will return instances of the defined class and not dumb stdClass objects. Then you can define your own methods there.

See http://www.trellon.com/content/blog/creating-own-entities-entity-api for an example.

This feature will be in Drupal 8 (already is and core is currently being ported to it).