Toilet water running when full.
As I see it, this can be one of a few things.


Leaky flapper, which has already been suggested
Pull chain is too tight allowing water to seep under the flapper
pull chain too slack and can get caught under the flapper. 
Water level too high allow water to drop into the overflow


I'd replace both the ball cock and flapper, it'll run you about 15 bucks if you do it yourself. It's very easy.