Power adapter connection issues
Even if there isn't any obvious cable damage or bulging, the adapter could be failing. If the adapter is not one of the newer L-Shape Magsafe plugs, the need for a SMC firmware update is moot, but it's helpful to have the system up to date regardless.

Have you confirmed if a second, known-good adapter works on your Mac?

Updated: An SMC reset can also correct magsafe LED issues. http://support.apple.com/kb/HT3964