There were many discarded theories. Some examples are:
The theory of "caloric fluid" or "quantity of heat" which postulated that heat is a kind of special substance which can flow from one body to another on contact. It was widely accepted at the time when Carnot wrote his famous paper, and did not prevent him from making his fundamental discoveries. But soon it was proved wrong and discarded.
The theory of phlogiston in chemistry, explaining combustion.
The theory of aether in electromagnetism. (Funny remark: for English speakers, radio waves are "in the air", while for Russian speakers they are "in the aether", which is still wrong but closer to the truth:-)
The theory that "nature abhors the void" of Aristotle, according to which vacuum does not exist in nature. This theory explained the working of water pumps, until they started making very large pumps. (Nowadays we have a very similar Principle: "Nature abhors naked singularities" (due to Penrose) but this has not been discarded yet).
Descartes' "theory of vortices" as an alternative theory of gravitation, accepted by many scientists at the time of Newton.
The ancient Greek theory of vision which assumed that our eyes emanate some rays that somehow feel the objects (like tentacles, or perhaps like radars). This was widely accepted and did not prevent the Greeks from developing essentially correct rudiments of geometric optics.
Newton's theory of air resistance (modeling air as a collection of hard balls bouncing from the surface of a moving body). It was accepted until the end of 19th century, and made many physicists believe that airplanes are impossible (it gave a wrong formula for the lifting force). The correct theory was developed only at the time when the first airplanes started to fly. (Later it was found that Newton's theory gives a good approximation for hypersonic speeds.)
Eudoxus' theory of homocentric spheres supposed to explain the motion of planets. Also Ptolemy's theory of celestial spheres, explaining the distances of planets from the center of the world, which unlike his epicycle theory proved to be untenable.
Galileo's theory of tides (which he considered the main proof of the Earth rotation) turned out to be completely wrong.
Titius - Bode Law describing the planet distances. When I went to school, it was still considered a valid law, and efforts were spent to justify it theoretically.
Remarks. After having read some comments, I decided to explain what I mean by "wrong". Most scientific theories describe only parts of reality and only approximately. So we develop more general and more precise theories. This does not make our previous theories "wrong": they still describe well certain classes of phenomena with sufficient accuracy.
For example, Newton's mechanics and gravitation theory were "superseded" by Special and General relativity but this does not make them wrong. We still use Newton's mechanics in most cases.
Indeed, why would we teach a "wrong theory" on all levels from primary school to university?! And why would we continue research on a "wrong theory"? Because people who construct bridges and airplanes and plan and control space missions use Newtonian mechanics!
So my definition of "wrong" is "has been discarded". In this sense, Newton's mechanics, Bohr's theory of the atom, and even Ptolemy's epicycle theory are not "wrong"!