Run iTunes without it being in the dock I'm trying to keep my dock simple - just Chrome, MacVim, and the terminal. Is there a way to run iTunes without it being in the dock (i.e. just show the icon in the menu bar)?
The only way for an application to not appear in the dock (while also keeping the menu bar) is for the developers to place that functionality into it. I don't use my dock as a launcher, using Butler instead (which is a dockless application, btw).

You might try backing up a step and asking why you want to remove the iTunes from the dock and see if there's another solution. For example, I often listen to tunes on my iPhone rather than iTunes. If it's to keep the dock clean, try a different launcher than the dock and hide the dock instead.