Up to the GM and particular RP.

I think for the most part a lot of rps on here expect the GM to guide the story, and considering how it's their rp, and their setup and world etc, that's not unexpected. However I encourage my players to add to and contribute to the story when and wherever they can simply because I find that a more interesting and fun prospect that keeps me on my toes when it comes to developing the plot. If only I was telling the story, and my players simply wrote reactions to that with their characters, it would get boring incredibly quickly, and I might as well just write a novel instead.

In my rp, I encourage co-gm chapters. What that means is, for most of the chapters I would take the leadrole when it came to a chapter's story, plot and theme, even still with the allowance of players to guide and propel the story in ways they'd like, and then at other times have co-gm chapters, where one of my players would take the lead for a chapter with me backing them up in order to let them tell and contribute a story they'd like and help develop their characters further, etc.