Updated: May 31, 2008
This is not a rant about Debian vs. Ubuntu. I used both, loved both, and I'm currently using Debian Lenny. It's not about Debian versus any other distribution either: in fact, I only tried a few other distros, and most of them were Debian-based. Here are the top 10 reasons for which I enjoy using Debian:
APT (Advanced Packaging Tool) is Debian's package management system. Installing an application is as simple as 'apt-get install amarok' and fetching all the updates can be done with 'apt-get update && apt-get upgrade'. Of course, there are APT frontends like Synaptic, if you're more comfortable using a graphical application.
Community is great, and I'm talking about both the forums at forums.debian.net and the official #debian channel on OFTC. Debian still has a channel on Freenode, which actually has more users than the official one (an average of 800 compared to 350 on OFTC).
LE: I almost forgot: mailing lists are another way of getting responses to Debian problems and discuss any aspect related to it.
3. Releases are rock stable
The release cycle is slower than other distributions, but the applications included in a new release are well tested and stable. You have the certainty that if you install the Debian stable release, you can trust it for security and stability, which makes it very fit on servers too, not only on the desktop.
4. It's been around from the beginning
If I'm not wrong, Debian and Slackware were the two big distributions which started just after the first version of the Linux kernel was released. What advantage constitutes this? Well, the community is comprised of both new and older, more experienced users; there are probably hundreds of projects out there based on Debian, which can only contribute to it (take Ubuntu for example).
5. Debian usually ships with default settings in applications
So you will be able to start from the same default configuration and make it work your own way. I like this one because I usually like applications like Konqueror for example to come with their original default settings, and if I want to configure it another way, I can do it manually. Debian gives you full control over this.
6. It supports equally both KDE and GNOME
In fact, it supports any desktop environment equally since others, like Xfce, are also included in the repositories. This means no package is left behind or ignored, they are both tested to be stable and bug-free when a new Debian stable release arrives.
7. I got used to it
This is a more 'personal' reason: since my first distribution was Ubuntu, then Kubuntu and finally Debian, I got used to it. I think it wouldn't be hard for me to learn using emerge or rpm, but I'm more comfortable in something which I already know how to use.
8. I like the name
'You call this a reason?', you may ask. Yes! Actually, I was thrilled when I found out what Debian stands for - it's a combination of the names Ian Murdock (founder of the project) and his then-girlfriend, Debra. Hence, Debian!
9. Development model
I like that you can choose what version you want to use. If you really need well-tested software and the best security you can get, use stable (currently 4.0, Etch), if you want newer packages, then use Testing (currently Lenny).
Debian is one of the few distributions which benefit of hundreds of dedicated websites with documentation, not to mention personal blogs. The official documentation found on Debian's website is also abundant, and I always take a look there every once in a while. And, I almost forgot it: there is the Wiki, there are the forums, and there is IRC (#debian on OFTC). And if you really need an answer very fast, you can always try the UbuntuForums, since most of the solutions provided there work flawlessly in Debian.