Just in case you are not very experienced with C++, be careful about multiple inheritance (also called diamond of death) when inheriting several class.
I found no practical reason to not have a class inherit CCObject : with CCObject, you benefit automatically from the ref counting and your object can be used in CCArray and CCDictionary (which I love). It’s also much like what you would do on Objective-C (which cocos2d-x is heavily based on), where every object inherit from NSObject.
The only reason would be, perhaps, a slight gain in performances. But if you find yourself in that situation, chances are the problem won’t be coming from CCObject.