Update (4/4/2013): Linux distros don't support Emoji very well by default, but you can simply install the Symbola font and that will make Emoji just magically work.
Apparently, Mac OS X Lion supports Emoji icons like iOS does.
Please, nobody get in the habit of using these. Anywhere. Unless you're talking specifically to other Apple users.
Nobody else supports Apple's particular variant of Emoji icons as well as Apple does. For Linux and Windows users, all your Emoji icons you paste in Twitter updates don't work. Most of the icons will be completely broken for these users (rendering as a block character), and the few icons that do render, won't look nearly as good as on Apple devices: they'll just look like Unicode characters, i.e. using the same black-and-white font color as everything else. Not full color icons.
It's already bad enough that cross-platform mobile apps (iOS and Android) have idiots using Emoji icons everywhere (which do not display on Android at all, but show as broken block characters), but for desktop Apple users to be able to paste Emoji icons everywhere else is just the most terrible news as of late.
Don't use them. Period.
The album is here: http://imgur.com/a/WAKF2