I uninstalled almost everything, and then tried reinstalling the Sun Java JDK, the BlackBerry Java Application Development Environment, and the BlackBerry Web plug-in for Eclipse in Windows XP Mode. Windows XP Mode is basically a Windows XP Virtual PC with some Windows 7 desktop integration. Because of the way XP Mode installations are detected for the Windows start menu, only the JDE and the simulators showed up under the Windows XP Mode Applications menu, which makes them available as virtualized applications that appear to run on the Windows 7 desktop. The Eclipse installation has to be run from within the XP Mode Virtual PC.
It took one more step to get the JDE to build applications: I had to manually add the JDK bin directory to the XP Mode path. But once that was done, I was able to build all the supplied BlackBerry Java applications and, eventually, debug them in a simulator. I say "eventually" because the performance of the simulator is noticeably slower in a Virtual PC than running on the Windows 7 desktop. I'm looking forward to "real" Windows 7 support.
I didn't get to run the applications on my physical BlackBerry Tour device; it appears that to load applets onto the device, they need to be signed. As I'm just testing the waters, I don't yet have a BlackBerry code signing certificate. If and when I get serious about BlackBerry development, I'll have to order one. Meanwhile, the simulators appear to be quite faithful to the real devices. In fact they're quite impressive, as you can see in the screen shot below. (Click on the image to see it full size.)