It must be made clear that independent or indie films are not within a genre in themselves.
That said, I leave my selection of films that at the time had a low budget, or low audience, but a lot of talent, great firsts, and innovative ideas within the cinematographic world. It may be that right now you see one on the list and think that it is mainstream, the truth is that perhaps now it is already a cult movie (which is not a genre either) and therefore popular.

If you have any in mind that you think should be on the list, comment on it, folks,