I don't think that the anxiety is typically induced by the content of the message one is giving. Rather, it's the self-presentation, the exposure, the potential for total public humiliation, that causes such terror.
But it doesn't need to be that way. In fact, I think its entirely possible to enjoy public speaking, and to do a good job of it.
The key is what I term "decentralizing yourself." This means to shift the emphasis of your talk from the messenger to the message. It's amazing how easy it is to confuse these two things.
When all eyes are on us, we have a tendency to feel the collective pressure of the audience, to palpably feel the social judgment that is likely being cast on us, and to ask ourselves, "Do they like me? Do they think I'm a stammering idiot?"
But here's the key: it's not about you. Or at least it shouldn't be. Let your message take center stage. The first crucial element here is to have something worth talking about. But assuming you have that, then take yourself out of the center of the frame -- "decentralize" -- and let the importance of your ideas take center stage. Let your persona be only a conduit that allows the subject matter to entertain, educate, and inspire.
In my experience, paradoxically, it's only this self-decentralization that allows you to really shine. It's the temporary abdication of ego that lets the self shine most brightly, a spiritual truth that applies to much more than just public speaking.
So next time you have to give a talk, remember this: don't tell a lame joke about how much you have dreaded the occasion; have something worthwhile to speak about; and as you prepare and before you actually speak, tell yourself over and over, "It's not about me. It's not about me."
Then go stand and deliver, baby. Give 'em something to remember.