We are a long way off but wheels are in motion for the 3rd film already:
Release Date - June 10, 2016
Sony Enlists Writers for The Amazing Spider-Man 3
Having set a release date for the movie a few months ago, it's no surprise that Sony has now hired writers to pen The Amazing Spider-Man 3. According to The Hollywood Reporter, Alex Kurtzman, Roberto Orci and Jeff Pinkner have been brought back to script the third part in the series which is currently set for release on June 10, 2016 with a fourth film in the franchise to follow on May 4, 2018.
Andrew Garfield is expected to reprise his role as Peter Parker in the film, but what supporting cast and villains will appear remains to be seen. It is also unknown at this time if director Marc Webb will return for the third movie.
Hopefully a better villain for the 3rd film.