Can you get any of those three frameworks to expose arbitrary views? One of my biggest complaints with all of them is that they seem to only expose objects.
When you say objects I assume you mean model objects? In that case yes. I haven't used Piston or Tastypie in awhile, but I know that you can easily write views in django-rest-framework that aren't tied to models.
This is a bullet from the django-rest-framework page I linked above: "Modular architecture - MixIn classes can be used without requiring the Resource or ModelResource classes."
I read through both of those links and I think I wasn't clear with my initial question.
I want to expose arbitrary view methods to GET calls, not linked to any model, and not have to write a new class for every view I want to expose. Basically I want views to return the correct filetype (json, html, xml, etc) when requested. This is basically making django a little more rails-like. I'm leaning towards django-dynamicresponse currently.
I really like how the three you mentioned tie into Django's forms though, and that's quite a feature to give up.
Yes, you can get djangorestframework to be used without being tied to any model, or even without tying it to a resource. In its current incarnation, djangorestframework just follows the principle from generic class-based views.
You just define a view that inherits from djangorestframework.views.View, and implement the action methods (get/post/put/delete) that you want. These methods must return a dictionary, and the framework handles the part of dispatch and render the view in the proper format.