An M:TG Question (Mind Control Effects)?

I've a question about the general Mind Control cards. Not necessarily Mind Control cards, but effects such as "gain control of target creature". When you DO gain control of said creature, do any enchantments and equipment on it come over with it? Also, does this differ any if you chose to take a creature from a "gain control of target PERMANENT" effect? As in, if you gained control of target creature via gaining control of a permanent, do the enchantments and equipments come over in that case?