I am not expert, but it seems that Nash's embedding theorem is considered very unexpected for two reasons: first because at that time people thought that Riemannian manifolds were a so general object that nobody thought that they could be actually embedded (as smoothly as possible) in an Euclidean space. Second, because Nash's proof used new and unexpected technique. If you read Gromov's interview for the Abel prize http://www.ams.org/notices/201003/rtx100300391p.pdf, at p.394, second column, third answer, he said: At first, I looked at one of Nash’s papers and thought it was just nonsense. But Professor Rokhlin said: “No, no. You must read it.” I still thought it was nonsense; it could not be true. But then I read it, and it was incredible. It could not be true but it was true.

I am not expert in the field, but it seems that Nash's embedding theorem is considered very unexpected for two reasons: first because at that time people thought that Riemannian manifolds were a so general object that nobody believed that they could be actually embedded (as smoothly as possible) in an Euclidean space. Second, because Nash's proof used new and unexpected techniques. If you read Gromov's interview for the Abel prize http://www.ams.org/notices/201003/rtx100300391p.pdf, at p.394, second column, third answer, he said: At first, I looked at one of Nash’s papers and thought it was just nonsense. But Professor Rokhlin said: “No, no. You must read it.” I still thought it was nonsense; it could not be true. But then I read it, and it was incredible. It could not be true but it was true.