According to Dive Into HTML5, (today, 27/09/13) the required attribute is supported in
- IE 10+
- FF 4+
- Chrome 10+
- Opera 9+
(not in Safari, not in Android)
Maybe you should implement a fallback feature in Javascript, anyways, until this gets better cross-browser support.
EDIT (to reflect Mr Alien's comment): You should also always have a Server-Side validation feature, because Javascript can be disabled or edited quite easily.