There's two parts to this question, really.
Q: Which browsers support the "async" attribute on a script tag in markup?
A: IE10p2+, Chrome 11+, Safari 5+, Firefox 3.6+
Q: Which browsers support the new spec that defines behavior for the "async" property in JavaScript, on a dynamically created script element?
A: IE10p2+, Chrome 12+, Safari 5.1+, Firefox 4+
As for Opera, they are very close to releasing a version which will support both types of async. I've been working with them closely on this, and it should come out soon (I hope!).
More info on ordered-async (aka, "async=false") can be found here: http://wiki.whatwg.org/wiki/Dynamic_Script_Execution_Order
Also, to test if a browser supports the new dynamic async property behavior: http://test.getify.com/test-async/