Answer: A surprising number of plants can be toxic to pets (and people) if eaten. If you have a dog who eats plants often,you may want to create a separate plant-free dog run area for the dog to be in when you are not able to supervise.
Here are some lists you may find helpful as reference. (You may need to cut and paste the complete url into your browser to make it work correctly.)
Humane Society List
You might also want to check with your veterinarian for suggestions.
Q&A Library Searching Tips