Almost all of the sites we buildat Ugli are built on Drupal, and to some extent I've become an evangelist for the modular, open source CMS framework. Generally speaking, evangelists that you disagree with are annoying so I think it is probably worth explaining why I love Drupal so fervently, and attempting to compare it with the custom-built CMS solutions I used to prefer.
(I will assume that the requirement for a CMS of some sort is acknowledged and omit the arguments for using a CMS over a static HTML site. In my experience 98% of web projects will ultimately benefit from a CMS, but this discussion is for elsewhere.)
See the Drupal Wikipedia article for a good grounding of what it is.
It's free
This might sound obvious but it is sometimes overlooked as one of the key benefits. Custom solutions are not free (they need to be built), and most other available Content Management Systems are paid-for. The elves at Drupal have put together a world-class content management system which you can download and use totally gratis.
A custom CMS project would necessarily begin with the development of swathes of functionality which are already available (tested and, to a varying extent, documented) in a fresh Drupal installation and in easily installed modules.