In HTML5, you no longer need to include the type in a script tag when you are using JavaScript.
Are any common browsers (IE6+, Firefox 2+, Safari 3+, Opera 9+ or sim
No it won't break any of the popular browsers, including the ones you mention. The tag will work fine without the type attribute, because all popular browsers will default to JavaScript.
Quoting Douglas Crockford:
type="text/javascript"This attribute is optional. Since Netscape 2, the default programming language in all browsers has been JavaScript. In XHTML, this attribute is required and unnecessary. In HTML, it is better to leave it out. The browser knows what to do.