Instead, a window must have "focus" (meaning you've clicked in it to make it the selected window) for the mouse wheel to function. That's insane! Fortunately, there's WizMouse, which enables your mouse's scroll wheel to work in whatever window is under your cursor, plain and simple.
This clever bit of freeware (for which I'd gladly pay a few bucks) works as advertised. Wherever you point your mouse, the scroll wheel works. WizMouse can also optionally add wheel-scrolling capabilities to programs that don't support it.
Note to Microsoft: Steal this program! (Actually, pay the developer handsomely for it.) This is the way mouse-wheel scrolling should work, and it's not too late to add it to Windows 7 -- is it?
Thanks to reader ivan007 for sharing this tip!