Can we override Drupal includes files?
Generally Clive is right. Don't touch core. But sometimes you are forced to do a core patch or it's just much easier to solve your requirements.

If you must: I'd recommend to put your whole project into git. This gives you the possibility to have a clean core version in one branch and the patched one in an other. Everytime a new core version is published you can merge it in a clean way.