<p>I have a Tab Control with multiple Tab Pages. I want to be able to fade the tabs back and forth. I don't see an opacity option on the Tab Controls. Is there a way to cause a fade effect when I switch from one Tab Page to another?</p>

There is no magic Fade switch in the standard windows control.
You could dump the content of the tab to a bitmap (using
DrawToBitmap
or
CopyFromScreen
?), show that bitmap in front of the TabControl, switch tabs, and then fade the bitmap.