Is it a good idea to build RESTful API's as backends for the web, Android or iOS?

I suppose this question is rather general, so here it goes. When you look at the web, Android and iOS now - it seems like a good idea to code every backend as a RESTful API. Doing so would mean that an app designed for one platform, would not require the backend to be changed at all for any of the other platforms.

So my question is, is this a good idea? And is this what most websites are doing nowadays?