You CAN drink piss and it probably won't hurt you, but when you consider the actual chemical makeup of it, I don't know why in the hell you'd want to. Unless, of course, you were adrift in a liferaft or something.
Urine gets its name from urea, a hydrous ammonia compund. Also mixed in with urea, just to add some flavor, there are ketones, broken down bits of whatever indigestible liquid content you may have eaten or drunk, including but not limited to, alcohol, sugars, ionic salts and, if memory serves, dead white blood cells. It's not something I'd want to actually swallow personally. Taking it orally I could see, but not actively drinking it.
Feces is another story altogether. The health risks of feces are numerous. Many parasitic infections are passed through feces, as well as about five thousand strains of bacteria. The most malevolant of which is e coli, which does occur naturally in the human digestive tract, but below the stomach. It is when e coli is introduced into the stomach that you have all kinds of problems, like FindingFantasy was saying.
I would definitely not recommend ingesting feces or even putting it into your mouth. It's just not worth the risks.
You can also visit the other thread on this very subject and read mine and other peoples' posts on this topic, here.