I'll try to give an answer that adress what you say.
First of all the biggest physical object I know of, is
http://en.wikipedia.org/wiki/VY_Canis_Majoris we're talking an object that if put in the middle of the solar system would engulf the sun and all the planets up to saturn and a bit further.
However, such an object that weights in at close to 30-40 times the sun, is extremely tenuous, we're talking about a star who's density is incredibly small, thus the problem of accurately measure it, since at some point we're basically trying to measure an object that is less dense then a fly's fart in space.
Such an object measures close to 1,7 billion miles, and it would require light over 2 and a half hrs to go across, and nearly 5 hrs to go around it.
Considering how massive it is and its awesome radiation, you might want to be further away from it when you go around it tho :)
The main problem with any "stellar scale" structures, that you would find in science fiction, since we can't build them atm, is that you always encounter the same barrier, the torque, the forces and the stress impossed on the structures invariably call for material with strength and specific requirements completely out of this world, and far far beyond even our best possible technologies.
Consider just a ring world, not a full scale Dyson sphere, but just a belt built around a sun, for example this...
http://en.wikipedia.org/wiki/Ring_world
When you want to conceptualise such structures, you always find that the laws of science and the capacity of our technology simply can't allow for such object.
As far as a natural object, like i said, the biggest physical one are massive stars, otherwise, there's the lyman-alpha blob and forest are on a scale completely breath taking, but its not very tangible as far as object goes :)
Hopefully I answered your question a little.