All of our currently 6 Linux servers run Debian. There are web, file and DNS servers, a streaming server and more. Planned projects using Debian include have it run mail services as well as to replace our currently LRP based router.
Debian replaced other Linux distributions mainly because of its ease of use and administration. Security updates or even updates from one release to its successor are as stable and easy as can be.
Besides a fully operational network of diskless clients, some of our normal workstations also run Debian every day already.