i'll tackle your question from the opposite side - there are relatively few things your dog shouldn't eat, such as (obviously) chocolate, onions, and grapes.
my own dog is a little "veggie hound", he loves all kinds of veggies and also fruit. he prefers steamed to raw, pulped veggies tho, so unless i feed pieces of raw veggies as a snack that's what i use. broccoli, sweet potato, zucchini and carrots are especially big hits. his favorite fruit is banana, but you can also hand him a whole apple and he will eat it completely. in each batch of food i prepare for him i use 3-4 different kinds of veggies, rotating frequently.
one thing you need to be aware of is that dogs cannot break down the cell walls of most raw fruits and veggies. if you give your dog a whole, raw carrot for example, you will see bits of undigested carrot in her poop.
in order to be not just a snack without much nutritional value, these cell walls must be broken down, either mechanically (pureeing, mashing, grating), chemically (freezing, cooking, steaming etc.) or by enzymes (e.g bacterial fermentation, digestive enzymes).