MDN has the following about basic support:
- Chrome 38 and up
- Firefox (Gecko) 13 and up,
- Internet Explorer 11 and up,
- Opera 25 and up,
- Safari 7.1 and up
Other features may or may not be available, see the linked page for reference.
It is part of the ECMAScript 6 specification, so you it will be well-supported in the future, but right now, I would not depend on it. But you might use a tool to convert your ECMA 6-complaint code to ECMAScript 5, as it is backwards compatible.
solved Is the JavaScript Set data structure supported by all the browser?