System Information
Windows 7
NVIDIA GeForce GTX 660 Ti
Blender Version
Broken: 2.75a c27589e (But if I can recall correctly this bug has been around for a while)
Short description of error
The composite node will not update the "Render Result" unless the "Render Result" is open in a window while blender is composting.
So if you don't have the "Render Result" open in a image editor the composting will not take affect.
Made a quick video demonstration as well:
https://www.youtube.com/watch?v=afmlNH2CUHk
I realized some of the text in the video might appear a bit fast, but you'll just have to use the pause button if you want to read it.
Exact steps for others to reproduce the error
https://www.youtube.com/watch?v=afmlNH2CUHk