obsolete scientific theory

An obsolete scientific theory is a scientific theory that was once commonly accepted but (for whatever reason) is no longer considered the most complete description of reality by mainstream science; or a falsifiable theory which has been shown to be false. This label does not cover theories that are yet to gain wide support in the scientific community (protoscience or fringe science). This also does not cover theories that were never widely accepted, or theories which were only supported in specific countries because of the imposition of dictatorial regimes (such as Lysenkoism). In some cases, the theory has been completely discarded. In other cases, the theory is still useful because it provides a description that is "good enough" for a particular situation, and is more easily used than the complete theory (often because the complete theory is too mathematically complex to be usable). Karl Popper suggested that all scientific theories should be falsifiable otherwise they could not be tested by experiment. Anything which cannot be shown by experiment to be false would therefore be an axiom and have an absolute status, beyond any refutation.

Obsolete biology theories

Lamarckism - but revitalised in Neo-Lamarckism - see also epigenetic inheritance
Miasma theory of disease - obsoleted by germ theory of disease
Spontaneous generation (abiogenesis)
Recapitulation theory - or "ontogeny recapitulates phylogeny"

Obsolete chemistry theories

Caloric theory
Phlogiston theory - replaced by Lavoisier's work on oxidation

Obsolete physics theories

Aristotelian theory of gravity - discredited by Galileo
Aether - failed to be detected by the Michelson-Morley experiment, made obsolete by Einstein's work.
Plum pudding model of the atom - assuming the protons and electrons were mixed together in a single mass
Emitter theory - another now-obsolete theory of light propagation.

Obsolete astronomical and cosmological theories

Ptolemaic system/Geocentric universe - obsoleted by Copernicus and Galileo
Copernican system - obsoleted by Johannes Kepler and Isaac Newton

Obsolete geographical theories

Flat earth theory
The Open Polar Sea, an ice-free sea once supposed to surround the North Pole

Obsolete medical theories

Theory of the four bodily humours
Eclecticism (medicine) - medical history - Some say it transformed into homeopathy and pseudoscience.

Obsolete branches of enquiry

Alchemy, which led to the development of chemistry
Astrology, which led to the development of astronomy
Phrenology, was once widely studied but now considered a pseudoscience
Numerology, as distinct from number theory, now considered a pseudoscience

Approximate theories

Here are theories that are no longer considered the most complete representation of reality, but are still useful in particular domains. For many theories a more complete model is known, but in practical use the coarser approximation provides good results with much less calculation.

Steady State - The Big Bang and dark matter threaten to destroy this comfortable world picture.
Universe - The possibility of Multiverses is one of the consequences of cosmic inflation.
Atoms are no longer thought to be indivisible, but are now seen to be composites.
Nuclei disintegrate at high energy.
Heliocentric universe theory - This is still used in the coordinate system of celestial mechanics.
Newtonian mechanics - obsoleted by Theory of Relativity and quantum mechanics. Still useful in engineering and physics at either middling (human) scales or where appreciable fractions of the speed of light need not be considered.
Bohr model of the atom - Allows for exact solution of the hydrogen atom, but larger atoms are not well described.
Newton's sine-square law for the force of a fluid on a body - no longer considered useful at low speeds, though it has found application in hypersonic flow

Theories whose significance was overstated

Land bridges - Though temporary connections between land masses sometimes allowed migrations (as when sea levels were lowered during ice ages), the actual splitting of continents by plate tectonics has been more important.