Core hacking is not attempting to force your way into the Joomla! core, but adjusting the Joomla! core files (i.e., the files that you uploaded before installing Joomla!), which should actually be hidden from and left alone by users and extension developers. Any changes you make to core files will be overwritten during the next update, which means that you will need to reapply your core hack. See Understanding Output Overrides for information on a mechanism to adjust Joomla's output permanently without hacking the core.
If you want to add a core hack to this Wiki, please add Template:CoreHackNotice at the top of the page.