Short answers, pulled from the story.
Einstein's central thought experiments include the magnet-and-conductor asymmetry that drove him toward special relativity, the falling man that led to the equivalence principle of general relativity, and the 1909 mirror-in-a-cavity argument that demonstrated wave-particle duality. His 1935 EPR paper, built on a thought experiment about two correlated particles, identified the phenomenon of quantum entanglement.
Two thought experiments were decisive. Einstein found it unbearable that moving a magnet near a wire and moving a wire near a stationary magnet produced identical currents but required completely different theoretical explanations. Combined with the conflict between Maxwell's fixed speed of light and Newtonian mechanics, these puzzles drove him to propose the two postulates on which special relativity rests.
Einstein described the realization he had in 1907 as the happiest thought of his life: a person falling freely from a rooftop would feel no gravitational field in their immediate vicinity. This insight, the equivalence of gravitational and inertial mass, launched his eight-year development of the general theory of relativity.
The EPR paradox is a 1935 thought experiment by Einstein, Boris Podolsky, and Nathan Rosen arguing that quantum mechanics is incomplete. Two correlated particles that have interacted retain linked properties even when separated; measuring one fixes the properties of the other regardless of distance. Einstein argued this meant the second particle must possess definite properties at all times, which quantum mechanics did not account for.
At the Sixth Solvay International Conference on Magnetism in 1930, Einstein imagined a box that released a single photon through a fast-acting shutter, arguing that weighing the box before and after and knowing the moment of release would allow both the photon's energy and its departure time to be known simultaneously, violating the Heisenberg uncertainty principle. After a sleepless night, Bohr replied using Einstein's own general relativity: the box's height change during weighing caused a clock-rate difference that restored the uncertainty relation exactly.
Einstein's EPR paper of 1935 identified quantum entanglement, the phenomenon now central to quantum computing, quantum encryption, and quantum information theory. In 1964, John Stewart Bell derived experimentally testable predictions from Einstein's local realist position; the first experimental tests carried out in 1972 falsified local realism and confirmed the quantum mechanical predictions the EPR paper had questioned.