Update: On October 20, 2009, Apple introduced the successor to the Mighty Mouse, the Apple Magic Mouse:

It eliminates the scroll wheel completely, so you’ll never have the scrolling problem again! The whole upper surface of the Magic Mouse is a multitouch touchpad. If you buy one through this affiliate link, I get a little percentage that helps me maintain this site and keep up on the latest technologies. Thanks!
A few times now, the Mighty Mouse on my Mac (the one with the tiny little scroll ball on it) has lost the ability to scroll down. It scrolls upwards, and horizontally, with no problem. Seemed like a software problem to me, and in the past, restarting the app I was using, or the whole Mac, seemed to fix the problem.
It started doing it again this morning, and this time, no amount of rebooting, unplugging/replugging, etc. would work. I figured it had to be a software (or maybe electronic) problem, since if it was just gunked up and dirty, I figured it would impair scrolling in all directions. Not just one.
Well, it turns out, when the Mighty Mouse scroll wheel gets dirty, it stops being able to scroll down. Apparently, it’s a common problem, as a quick Google search turned up tons of pages, like this one at MacOSXHints.com.
The fix? Blow compressed air around the scroll ball, or just push on it really hard and roll it around (that worked for me). If you’re lucky (I was), it will start working again. If it keeps doing it, though, I’m going to have Apple replace it.
What a weird problem. Design flaw? Who knows. I guess it would be better if it were easier to remove and clean the scroll ball. Apple’s official directions for cleaning it are “hold it upside down and roll it around”. Seriously. They even have a video to show you how to do it.