Can i "execute" the Compositor node graph without re-rendering? I have an image rendered, and its showing in the Blender Render window.
In the compositior, i have a file output node set up to write out .tif files for each render pass. Can i somehow execute just the node tree without having to re-render my image?

Ok, so the proposed answer said:
"Delete the renderlayer node from the node setup, and then blender won't render the 3D scene."

Feeling stupid here, but, if i remove the renderlayer node, then my file output node won't have any inputs anymore. It's direclty connected to the passes of the renderlayer node to output each pass as a .tif file.
Secondly, what button do i have to press to then execute only the compositor nodes??
If I understand your question, when you render an image and set "use nodes" in the compositor, you can check the "backdrop" function, then Ctrl Shift click on a node to create a viewer and see the output of that node on the backdrop. You can see the result anlso in an UV/image editor, if you change the header's dropdown menu from "render result" to "Viewer node".

As soon as you change a value in the compositor, the change is reflected in the Viewer (Backdrop or UV/Image window), without any need to push any button to trigger the compositor, and without the need of redoing the render: it's automatic (maybe a little slow and not realtime: check the upper info header for a compositing Time bar)