Chrome, as our main development browser, has full support.
Support for desktop versions of other modern browsers (Firefox, Opera, Safari, Edge (EDIT: Edge was postponed due to some critical bugs in it)) will be added in iteration 3 (it starts next week): https://github.com/ckeditor/ckeditor5/issues/201.
Mobile versions of browsers aren't currently thoroughly tested, but we see that the editor works there (I'm not sure how stable it is, though). We're still researching mobile UX/UI topics (see https://github.com/ckeditor/ckeditor5-design/issues/149) and most likely we'll work on a full support (in UI and editing engine) once that is concluded. There's little value in a working editing engine if the UI is not ready.
Moved from: https://github.com/ckeditor/ckeditor5/issues/236.