Not veterinary advice: Yes. Dogs can eat graham crackers. However, it is not advised to let your dog eat a good amount of graham crackers because they contain quite a lot of carbohydrates, and a regular diet high in carbohydrates would lead to obesity in dogs. Occasionally giving your dog a cracker or two should not be a problem.
Here are the 10 most dangerous items your dog can't eat according to About Doggies:
Alcohol
Avocados
Chocolate
Coffee, Tea and Caffeine
Fruit Pits and Seeds
Grapes and Raisins
Macadamia Nuts
Onions and Garlic
Xylitol
Yeast Dough
On the other hand, you can find the best food to feed a dog at Pet MD.
A nutritious, balanced diet is essential to keeping your dog healthy. Learn what you should be feeding your dog at every stage of its life (via Pets WebMD).