Depending on how obsessive compulsive you are, this tiny tool might be a god-send. Windows tends to build programs from left to right (away from the Start button) in the Taskbar as programs are launched. If you close a program and re-open it, it will go to the end of the line. If you want to be able to re-arrange the programs listed at the bottom of the screen, download Taskbar Shuffle.
This program does exactly what it needs to and offers all the options you’d want. It starts off as an icon in the system tray, but even that can be disabled. You simply drag and drop the programs in the taskbar. It’s the exact same way you can move tabs around within Firefox. It can also let you shift around the icons in the system tray or it can be configured to group programs together.
Update: Windows 7 and newer versions of Windows already come with this functionality without need for add-ons.