None of the files in
/developer/ in my root directory appear to have been modified in the past few years, even though I've been using XCode constantly since. Is it obsolete? Are the developer applications like Filemerge now stored somewhere else? Can I delete it?
Yes, it's obsolete. It has changed at Xcode 4.3.
Now everything is in the Xcode.app folder.
Apple talked about talked in their "What is New in Xcode 4.3" document:
/Developer No Longer Exists
The simplification afforded by repackaging Xcode 4.3 as a single app bundle eliminates the need for the /Developer directory containing prior versions of Xcode. As a result, the Install Xcode application and the uninstall-devtools command line script are also no longer needed.