Some breeds/individuals tear more than others. Sometimes it's anatomical (dogs with bulging eyes or blocked tear ducts), sometimes it's caused by ear infections, sometimes it's a reaction to low quality food or an allergy (food or environment), and I'm sure there are other causes for tearing. The stains themselves occur because when moisture sits there on the dog's face stuff (red yeast and bacteria) starts to grow there turning the fur reddish.
Most dogs that tear will continue to tear unless there is something like an allergy or being on low quality food that is causing it. Tucker has tear stains, but they were MUCH worse when he was teething, I think that is also a cause of tearing.