Specifically, textfac.es (or textfaces or text faces, I'm not really sure either) lets you finally write those damn unicode faces. You should probably bookmark it so you don't lose it. When you need a textface, just hit the bookmark, click the face, and paste it where you want it to go.
The click-to-copy works through ZeroClipboard, which uses Flash (I'm so sorry). If you don't have Flash, you'll have to highlight the faces like a caveman.
If the faces look weird or you see rectangles all over the place, you might not have the right fonts installed. Or the face might actually be weird.