I'm putting together a class on profiling web applications. We use PHP, so I needed to search around to find tools appropriate for that platform.
I picked Xdebug and kcachegrind. They make a wonderful combination. The output of kcachegrind is beautiful. Unfortunately, it appears that application has been abandoned since 2008.
For an example application to profile, I picked Moodle. Moodle open source, plus it is slow. It makes an excellent example for profiling.
Speeding up Moodle would be an excellent project for Google's Summer Of Code. Apparently there were 70+ people that applied to the program to help out Moodle. But I didn't see speeding up Moodle as an idea.