Didn't mean to sound picky. "Independent" literally means independent of a studio.
As far as independent production companies, there are hundreds of them, so it would be difficult to choose a favorite. The Weinstein Company - formerly Miramax - usually produces intelligent stuff. Mike Zoss Productions - the Coen Brothers' company - is another fave.
But you asked for a list -- did you Google search? As I say, there are hundreds.