I find the signal discovery scene from "Contact" to be one of the most inspiring moments in cinema.
The surprise, disbelief, then sudden realization, and then the creative chaos of trying to make sense of it and at the same time verify what it is... It just works on so many levels:
https://www.youtube.com/watch?v=u4iNWKfE-0k
https://www.youtube.com/watch?v=YM5MRUHi-gU
The whole film is amazing, too.