Before I purchase this game I want to know if the gog version has native xbox/gamepad controller support without the use of 3rd party apps. Can I get my xbox controller working from the game's settings?

Also, does this game have a complete storyline? In other words, without giving away spoilers are there any cliffhangers or "to be continued" type scenarios?

I don't think you should have any trouble using your Xbox controller with Psychonauts out of the box, especially since there is even GUI support for Xbox 360 controllers.

As for cliffhangers, well, the game is pretty much self contained; it has a story arc with a beginning, a middle and an ending and I, for one, was left very satisfied with the way it ends. There is, however, a minor scene during the ending cinematic that leaves enough open room for a sequel but, then again, it could simply be seen as Raz having graduated as a Psychonaut and now living the life one would expect a full-fledged Psychonaut to live. Every single story aspect the game begins to develop has closure, so I would say it doesn't end in any sort of cliffhanger and feels very much like a finished, superbly polished product that delivers on all fronts.