First of all, I like the idea that Debian is maintained by a group of dedicated people with a similar development model to that of the kernel. There is a “stable” release and an “unstable” release. I tend to build systems that are production back-office systems, and stability is a large concern. The main thing Debian brings to the table for me is its ability to update a running production system, in-place. This includes the networking code. The packaging system is careful to preserve your local installation parameters. I have found it worth the effort to learn dselect, the Debian package maintenance tool. Although it seems complex at first, I like the Debian package strategy, which provides requirements, suggestions and also conflict information for each of its packages. That, coupled with its fine granularity, means I can choose only what I need to be installed, know I have all the prerequisites, and be assured that packages won't be conflicting with each other. I hope the new package installation tool, Apt, due to be released soon, will continue to provide these features.
I started out with Yggdrasil Linux before kernel 1.0, went through several versions of Yggdrasil, several versions of Slackware, a couple of versions of Red Hat, and have finally been through Debian since before 1.0 and settled with Debian. I designed and ran a local ISP for three years, starting with Slackware, and moved to Debian to gain the capability of updating the production systems in-place. Trying to do this with Slackware was excruciating and caused us to delay important security fixes and updates. Debian has worked very well for me, and has never missed a beat when updating my systems. Providing stable 24 x 7 service is a very high priority. Other distributions may have added some of Debian's package functionality recently; I just haven't kept up to date with their features.
If you are searching for a Linux distribution, take a close look at the type of system you are implementing and how it will be used. The great news is there are many fine robust choices, each tuned to a particular need. Debian works well for me for my back-office server applications. But, if I needed to implement a secure web server, I would take a close look at Red Hat, especially if there was a client involved who needed vendor support.