Newtonian physics to relativity. Geocentricity to heliocentricity. Early chemistry to more modern atomic theories, and then to quantum theories.

There are also non-scientific examples, like streetcars to automobiles in the early 19th century.

Paradigms are usually theories in which an older scientist who has invested a great deal in the old paradigm is reluctant to switch to the new paradigm, and often explains away errors with preposterous explanations, much as one tries to rationalize post-hypnotically.