Watch the Open C Tuning Part 1 online guitar lesson by Richard Gilewitz from Fingerscapes
One particular advantage of the open C tuning is the deep resonance of the low bass note available since it is tuned down 2 full steps. Additionally, as in open D tuning with the D's in it's makeup with the root in the bass, the same goes for open C tuning.
This tuning is unique in it's dual suitability for either a bluesy sound or an ethereal, almost new age or classical sound with a plethora of rich chiming harmonics, particularly on a 12 string guitar.
You may also want to try an open C unison tuning where the 1st string is brought down 2 full steps from E to C. This creates a unison sound between strings 1 and 2 and by eliminating the 3rd in the triad a modal or droning sound occurs.
Yet another tuning is open C9 where the 1st string is only brought down one full step from E to D. Guitarist Peter Lang has composed some wonderful pieces in this tuning.