Summary:
This one's easy to reproduce. In new versions of blender, while the compositor works when a person does a render, if you change the linkages on the nodes in the compositor after doing the render, you can see the changes occur within the nodes editor itself, but not on the output image; you have to re-render to see them. This does not occur on older releases of blender.
Steps to reproduce:
1. Run Blender (default scene)
2. Choose Cycles render engine
3. Render (F12)
4. Go to the Node Editor
5. Select Compositing
6. Enable Use Nodes
7. Add a really obvious filter, such as Add -> Color -> Invert
8. Connect Render Layers (Image output) to Invert (Color input)
9. Connect Invert (Color output) to Composite (Image input).
10. Wait for it to finish compositing so that you can see the changes within the node editor.
11. Press F11 to look at the output image.
On Linux (older blender):
Linux version 2.6.31.1-56.fc12.i686.PAE
NVIDIA-Linux-x86-275.09.04 / Bumblebee (8 june 2011)
Blender 2.66a / 266.1 r55057
Result: Output is white (as it should be)
On Windows (brand-new blender):
Windows 7 Ultimate
Service Pack 1
Nvidia GeForce GTX 660
Blender 2.69 / 2.69.0 r60995
Result: Output is gray the gray cube, just like the original render