Alderson disk
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An Alderson disk (named after Dan Alderson, its originator) is an artificial astronomical megastructure, like Niven's Ringworld or a Dyson sphere. The disk is a giant platter, like a CD or phonograph record. The sun rests in the hole at the center of the disk. The radius of an Alderson disk would be roughly equivalent to the orbit of Mars or Jupiter, with a thickness of several thousand miles. According to the proposal, a sufficiently massive disk would have greater gravity than its sun. Close to its surface, the gravity of the disk would closely approximate that of an infinite flat plate, for which gravity is perpendicular to the surface. (Of course, near the inner and outer edges of the plate, edge effects would become significant.) The mechanical stress within the disc would be far beyond what any known material can stand.
Life could exist on either side of the disk, although the closer to the sun one would get, the hotter it would get until life was impossible. Conversely, the further away, the colder it would become, until living beings would freeze.
One drawback to a disk is that the sun remains in the same place. There is no day/night cycle, only a perpetual twilight. This could be solved by forcing the sun to bob up and down within the disk, lighting first one side then another. (As the disk far outmasses the sun, this is a plausible option.)
An Alderson disk (the Godwheel) was a prominent feature of Malibu Comics' Ultraverse. The Godwheel was split between two societies, one which used technology and one which used magic (each occupied separate sides of the disk). Author Larry Niven designed the Godwheel and wrote stories surrounding certain events on it.
A disk-shaped planet similar to an Alderson disk (though far smaller) served as the home world of the fantasy "Aysle" setting (or "cosm") of West End Games' Torg roleplaying game. In contrast with the Alderson disk, the Aysle "diskworld" works according to fantasy physics, including a "gravity plane" that bisects the disk laterally, so that opposite sides "fall" towards the plane. The diskworld of Aysle had a bobbing sun and multiple inner layers. Both sides of the disk were inhabited, as were the internal layers.
The Alderson disk is discussed in Larry Niven's "Bigger than Worlds" essay, 1974, which can be found in his "Playgrounds of the Mind" anthology.
