My answer to the cat litter question lists the hazards associated with cat feces. (Toxoplasma gondii, Fecal Coliforms, roundworm.)
Thanks to the University of Wisconsin extension for describing the hazards associated with dog feces:
What is the hazard in dog manure?
The common large roundworm, called Toxocara canis can also infect humans.
What kind of symptoms would a person have who is infected by dog worms?
- A condition called Visceral Larval Migrans. The ascarid eggs hatch in a person's small intestine. The little worms or larvae get into the blood stream and float to the liver. They migrate in the liver and get to the blood stream that goes to the lungs. Some may enter the general circulation and end up in different parts of the body. They have been found in the human heart, brain, spinal cord, skin, and other tissues. The symptoms would vary depending on where the larvae become attached.
- Another condition is called Ocular Larval Migrans. The immature ascarid worms or larvae can affect the human eye. The larvae attack the retina and cause blindness. Many eyes of children have had to be removed which until recently was the only treatment for this problem.
(Note that Toxocara canis is related to Toxocara cati which I listed in the answer to cat litter.)
However, don't let this make you think you can't compost cat and dog feces!
(Do this away from your vegetables/edibles as possible to avoid pathogen movement through the soil. Do not use the finished compost on edibles.)
It's organic material, pathogens and all, so it will break down given appropriate conditions. City Farmer has a page on composting dog waste. Among other methods, this is listed, along with a video:
About 15 years ago, I dug a hole in the back of my ornamental garden, away from my food crops. The hole is about 3 feet wide and 3 feet deep, and is covered with a plastic lid from an old compost bin. I empty my dog's waste in the pit every day so that it will break down as compost.
Occasionally I add Septo-Bac, an enzyme-active biological compound formulated to increase the digestion rate of sewage.
I am also starting to add some chopped yard waste (green and brown) to hasten the process. The finished dog waste compost can be used on ornamentals, but not on food crops. Dog waste is not allowed in garbage bins, so this alternative has served me well.
(If you watch the video, notice that she says she's got 10 years' worth of poo in the compost pit!)