To be fair, Emoji are a fairly recent addition to Unicode and they're not really ubiquitous outside of mobile phones (they started as a formal encoding of various pictograms used predominantly by Japanese carriers for SMS). No OS supplies enough fonts to cover 100 % of Unicode out of the box.

That being said, Emoji seem to work at least on Mac OS X (current) and Windows 8. Alas, Chrome doesn't render them within a page (but in the tab/title bar, maybe because the OS' rendering takes over there). Firefox and IE show them both, apparently (presumably because both are DirectWrite-based by now).