Taskix is a free utility that allows you to reorder the buttons in your Windows taskbar in-place using your mouse. If you have "Group similar taskbar buttons" set, it also works inside stacked groups.

Simply extract the files from the ZIP into a folder of your choice and start the EXE.

It is most straightforward to use - simply drag-and-drop the button you want to move - , it is fast and uses very few system resources. It also enables you to close programs from the taskbar with middle-click. There's a separate 64 bit version available on the homepage to use with 64 Bit Windows systems.

Taskix keywords: reorder, order, move, organize, drag, drop, dnd, taskbar, buttons, items, in-place, middle-click