Also known as a pressurized superplanetary sphere. This unusual kind of deep space structure is basically an enormous hollow shell whose shape is held rigid by gas pressure within. Using known materials such as carbon nanotubes and advanced composites, such a balloon megastructure could be built up to about the size of Jupiter and still remain structurally stable. However, smaller balloon worlds several hundred or several thousand kilometers across may prove much more practical to both build and maintain.
Unlike other megastructures which could serve multiple purposes, perhaps the only real reason for constructing a balloon world is to function as a habitat for life, provided it is filled with a breathable atmosphere. Light from its parent star could be let in through large transparent sections or through a series of gigantic gimbaled mirrors near its rotational poles.
The best example of such a construct can be found in Karl Shroeder's Sun Of Suns, a novella serialized in the magazine Analog from November 2005 through March 2006. The hollow world in his story was what he described as basically a "fullerene balloon" some 5000 kilometers in diameter, pressurized with breathable air and stocked with enough volatiles and organic materials within to equal the mass of Pluto. However, this mass is widely dispersed within the sphere, giving birth to a life-supporting but completely gravity-free environment. The makers of that world wanted to separate themselves from the rest of humanity, so they placed it far away from any star. In order to keep things comfortably warm for its human inhabitants and ecology, a great many radiative fusion plants, the "suns" of the title, were dispersed throughout.
Unlike other megastructures of such size, a balloon world need not be constructed of a hyper-tensile-strength material in order to function properly. Carbon nanotubes and like material, constructed in lattice-like layers for maximum stability and support, would more than suffice. In Schroeder's novella, the inner surface of the outer shell was unheated, allowing enormous mountain-sized formations of ice to condense along it from the cold of space. This layer of ice would provide an additional layer of insulation and structural support to the zero-gravity megastructure.
The means of air circulation within the balloon world would seem to be an issue. If left completely on its own, over a long period of time most of the gas and free floating material would "settle" in toward the mega-balloon's center of gravity, leaving large swaths of the habitat near the outer shell with diminished, and perhaps even unbreathable, atmospheric pressure. Machinery dedicated to circulation in the outer shell or floating about in the habitat itself could help to correct this problem. If the Balloon World supports a thriving ecology, its possible that ecology could be engineered to help redistribute the gasses and materials within more or less evenly over the inner volume. Alternately, the Balloon World could be set slowly rotating, with enormous interior projections or vanes to help stir up the inner atmosphere.
Distribution of heat would also become a concern, especially if the habitat were to support a self-sustaining ecology throughout its volume independent of its human inhabitants. Having large sections of the outer shell transparent to let in sunlight, or mirrors that could focus such sunlight on heat-exchange machinery on the outer shell, would be workable. The inner artificial "suns" of Schroeder's novella are another workable solution, but unfortunately would make living conditions within completely dependent on humans maintaining and building the fusion machinery. If the human civilization within ever fell or decayed to the point where such knowledge was lost, all life within could quickly become extinct.
Bio-engineering an entire ecology, whether human-dependent or not, adapted to a microgravity environment would be an enormous undertaking in and of itself. Ecologies are massively complex entities, and as our blundering about on our own planet has shown, they are often precariously balanced between thriving success and disaster. Recreating such a system in an environment where such life could never evolve naturally would present an enormous number of challenges, and may even require a significantly greater degree of technological prowess than would be needed to construct the mega-balloon itself.
Some science fiction works outside of Schroeder's novella have tackled some of the ins and outs of zero-gee ecologies. Among them are The Integral Tress by Larry Niven and Judas Unchained by Peter F. Hamilton.
Human society would also have to adapt. In "Sun of Suns", the inhabitants had to raise their children on enormous rotating town-rings that would simulate enough gravity to prevent birth defects and growth deformities that are often associated with zero-gravity development of organisms. Even so, they would probably never spend much time in Earth-like gravity conditions, and would invariably grow to be considerably taller and more spindly than their planet-bound cousins.
A balloon world could also be set spinning at a fast enough rate to allow pseudo-gravity on its inner surface along its spin equator. The gravity gradient would gradually drop off long the inner surface as one approached the poles. At this point the balloon world would in essence come a to resemble a vastly oversized Bernal Sphere.
"Sun of Suns", by Karl Schroeder, Analog, November 2005 through March 2006http://www.aleph.se/Trans/Tech/Megascale/megastruct.txt