We have Issue Tracking / Task Ticketing software for software development (we use Fogbugz) and are thinking about Issue Tracking for "other things" within the organisation - there are a couple of large projects going on at present and we need tasks to obtain budgets for licenses, hardware, and the like, find out from another company what PCs, Versions, blah blah, they use, pursue progress on things like getting the Server Room to be switchable between (electricity) phases ('coz one of the phases in the whole area keeping going down 
...) and so on. MAYBE?? even to progress HR issues (we have data confidentiality requirements on that ... so we might fall-short of including that).
Currently folk are using Email Inbox (crazy, CC: The World and no one knows who is responsible, someone overlooks something, noone can chase / oversee anything. There are then lists in XLS and higher managers, or where there are cross-over issues, things get copied into other-people's-XLS ... way too much String and Gum IMHO!!
I could, of course, just impose Fogbugz on them all. It allows "departments" and handles all the things like Assigned-To, Priority, Deadline dates and so on, so might well be "jsut the job". But I do look upon Fogbugz as being, primarily, intended for software development. If nothing else it might be a bit "Geeky" for ordinary mortals, and perhaps something MUCH more lightweight would be more appropriate (but I also favour "As few such APPs as possible")
What I think I need is:
Title / Description of the task
Assigned to only ONE person at a time
Allocate to Department / Project Categy/Sub_Category type hierarchy
"Notify list" of other people who need to know about it. People can remove themselves from anything which is / becomes irellevant
Priority, Deadline date etc. - maybe a Milestone Date expectation too
Flexible reporting so managers can do view "All the things/people I have a watching brief on"
Don't think I need any time recording (staff have to do time sheets, separately)
I'd be interested what you use, what you know of any would recommend and, equally as important!, what you would run away from!
