The House of Dreams

Well, I’ll have to defer to Jeremy Keith’s answer for everything about the Web: “It depends.” In my testing, support for any given Unicode character varies hugely (and by “support,” I mean that either the @font-face icon appears or that the underlying Unicode character appears, rather than the user seeing an empty rectangle or a question mark or nothing at all). Even Unicode characters in the same “block” of related symbols often have quite different levels of support.

But I can provide a little help. Once you know which Unicode character you want to use, run it through Unify, which will give you a support score based on the devices that I’ve tested with so far.
If you’re happy with either the @font-face icon or the Unicode character being displayed, you should see very high levels of support. Some icons work on everything that I’ve tested so far.
The big exception is Emoji characters, which I would stay away from. Around half of the devices that I’ve tested on don’t show the @font-face icon, and many don’t show anything meaningful at all.