The notion of parallel universes is more properly (and generally) termed multiverse. The term was first used by 19th century philosopher William James. It encompasses not only the universe that we are experiencing but also all other universes (either infinite or finite) that can also exist whether we can experience them or not. Different physicists/philosophers have postulated different possibilities for the number of universes in existence and how they interact including Max Tegmark, Brian Greene, John Wheeler, and Lee Smolin.
In terms of any actual scientific evidence to support the multiverse theory, there is none. Scientists are searching deep space for certain patterns in background cosmic radiation that would provide evidence of the collisions between different universes. But so far no evidence has been found.