Hooray!  I can now create, build, and run C and C++ projects through Eclipse on Windows.  Through my bug report to the Eclipse CDT team, it came out that CDT was locking indefinitely while interacting with gcc.  On my box, gcc is provided through Cygwin.  The problem, however, came up because, thanks to my Processing environment, my Arduino environment, and my WinAVR tools, I had multiple versions of the cygwin1.dll file.  When gcc was executing, it was picking up the wrong one and this was causing it to hang.  CDT would hang along with it.

The CDT team is looking into correcting this.  In the meantime, though, if you experience hangs creating a new project in CDT, I suggest you follow the advice in the bug report.  Try this command:

gcc -E -P -v -dD <workspace>/.metadata/.plugins/org.eclipse.cdt.make.core/specs.cpp

And see the result.  Gcc will report a pretty thorough complaint if you’re having a problem similar to mine.  At that point, you just need to hunt down and remove the extra cygwin1.dll files.  When I did this, it didn’t appear to ruin my Processing environment.  I haven’t checked my Arduino environment, and I’ll need to reinstall my WinAVR tools.

Of course, if I can’t have all the tools concurrently, I’ll have to switch from Cygwin to MinGW.