Oh, I don’t care about the order within my Mozilla tab that much… for now.
Guess I’m not that much of a hardcore fascist. hahaha…
Interestingly (or not), I’ve got my taskbar on auto-hide here at work, but not at home. This is because while I’m at work, I don’t want any authority figure leering over at my monitor and seeing that I’ve got an IE window for the SDMB minimized, or something. But it’s NOT on auto-hide at home, because if I’m not around the computer I keep everything minimized, but can check at a glance to see if I’ve got e-mail since an icon comes up in the system tray.
I, too, am extremely picky about my taskbar. Outlook MUST be the first button when I’m at work, and Microsoft Access MUST be the second button. IE is usually the third button (with the window open for my online classes).
However, it goes beyond even the order of the taskbar buttons. I MUST have the Quick Launch toolbar open at all times, and I cannot tolerate the MS Office Language toolbar. I don’t wear a watch or have a clock in my cubicle, so the Clock must also be turned on. I also LOATH the new WinXP thing that collapses the windows of the same program into one button, especially since I normally have multiple windows of IE and Access open at the same time.
I work at a university, and I teach in a variety of computer labs over the course of any given week. Our IT department does not believe that the Quick Launch toolbar should be part of the normal computer setup for the network, and the the Clock is often turned off. However, the *&^%$ Language Bar is ALWAYS there. (We don’t even have sound cards in most of the computers. WHY do we need the MS Language Bar???) On some computers, the Clock is turned off completely. 
I spend a lot of time at the beginning of each term tweaking the computers I use so that the taskbar is set up correctly.
Next term, though, IT is planning on installing software that will complete reset the computers every time they are rebooted, meaning that all personal settings on the network computers will be lost every day. 
For those of you who always want the icons in the same order, you should check out Taskbar Commander. I posted that before, but what I didn’t mention is that it can automatically arrange the icons in the order you like. So if you want Outlook Express to always be in a certain position, Taskbar Commander will automatically put it in that position whenever you open it. I think it can auto-arrange 25 applications.
Exactly. I sit where my supervisor can approach from behind, and while I don’t surf at work (I will if I’m on the phone on hold) I have a web browswer window open all the time because I update our division’s website almost daily, and sometimes several times a day. I feel cringingly guilty when someone comes up behind me and I’ve got a non-work browser open, even if I’m checking CNN while I’m on hold. I’d actually *like *to have a cubicle. So I like that taskbar to sink quietly out of sight when not in use. I also have the screensaver set to come up after a scant minute of inactivity.
Not that I’m paranoid.
I care deeply about the icon arrangement in the Quick Launch area, but not the actual taskbar programs. I tend to alt-tab through them, so it doesn’t much matter what order they’re in.
I don’t see it on the site: Do you know what OSs they support?
Reading this thread makes me feel so not alone. I feel almost normal in my oddity. Thank you Straight Dope! 
I work on several things at a time at work, so I have to have lots of stuff going at once. It helps if I keep things in the same order.
For example, for one project I need MS Vis Studio running for editting my progs, right after that WS FTP to send my source files to the Linux/UNIX platform it will compile and run on, then two terminal windows to the target platform, one for the server and the other for the client program. Repeat all for any other project I might be working on at the time.
Those progs that allow one to move stuff around might come in handy, thanks for those links folks.
TB: Acidmax (mIRC), Firefox
Tabs: SDMB, LJ, anything else.