I went to update CCleaner to the latest version, which is v5.41 at the time of writing this and it did not work. No matter what I unchecked or checked. I do not have Firefox installed, but I do have Chrome. I even went as far as to uninstall the old version first and install this new version in a clean manner. Even leaving the default item list the way it is and just hitting "Run CCleaner", it would still give me "the application CCleaner has quit unexpectedly". I am on Windows 7 and I do not have the extended .INI from the forums installed.
Now I remedied the situation by trying a bunch of different versions. I found that v5.39.6399 works without crashing.