Answer: It's hard to make such a list because there are thousands of plants and even if a plant is not poisonous, an animal (or person) can have a bad reaction to it. Here are sites that list poisonous plants:
http://www.ansci.cornell.edu/plants/plants.html from Cornell University.
I'd recommend staying away from oleander, which is often planted in the Southwest. All parts of it are poisonous and it can cause skin reactions just rubbing against it. Culinary herbs can make delightful additions to a garden and they shouldn't cause a problem.
As a pet owner myself, I suggest you grow some grass just for your dog to eat. Many cats and dogs love to chew on grass (perhaps it aids in digestion). They love oat grass, wheat grass, barley, etc. You can buy little containers at pet stores. Or, buy the unsprouted grain at natural food stores. Plant it in a soilless seed starting mix, keep moist, and place in sun. With very little training and encouragement, your dog might learn to eat from its own grass and leave plants alone! I hope this info helps.
Q&A Library Searching Tips