In the earlier versions of WordPress, the only way to change it’s behavior was to change the core files of WordPress. That was never considered as safe and was never simple for those programers who didn’t have much experience with PHP/MySql. However, with newer versions, WordPress started supporting both plugins & themes and with that the need to play around with the core files diminished.
Till version 2.7.x, WordPress allowed the programers to make changes in the core behavior, in indirect way by allowing them to add functions in my-hacks.php file. This way it kept the core files safe. Although, after the release of WordPress 2.8 the support for this file has been discontinued. I believe that the move is absolutely correct as there weren’t many users of this particular feature and if at all any functionality needs to be added, it can be done through themes and plugins directly.
The good news is that those who are interested in keeping this feature can follow these simple solutions posted by Frank @ WPengineer. By the way, have you ever used this option or ever made use of my-hacks.php file?