remove application from Windows taskbar

In Windows, normal application windows show up with a button in the taskbar, just the normal application button you see for virtually everything.. I know this is obvious, but I want to be clear about what I'm describing.

Does anyone know of a (freeware) utility that will allow me to remove the buttons of certain applications? There are a variety of utilities that will allow me to minimize applications to the tray, but I want the window to continue to be visible, just not have a button wasting space in the taskbar.

Use FireDaemon to run the program as a Service, then uncheck the little checkbox in FireDaemon that allows that service to interact with the desktop?

I know, totally weird and not exactly what you were looking for.

Heh. Neat idea. But FireDaemon isn't free any more, and I don't want to pay $5 for this feature, much less $39.

Old free version of FireDaemon still works.