You would want to consult reference books or google for reputable sites for lists for whichever particular critters you have in mind.
If you are specifically talking VEGGIE garden, though, you will not go too far wrong by simply avoiding all plants of the Solenaceae family (tomatoes, potatoes, peppers, eggplants) (obviously their fruits are ok, but the leaves and stems are not good to feed) as well as rhubarb leaves. Excessive amounts of dried mature legume seeds are not good either but that's unlikely to be an issue for you.
Other than that, as a general principle, if you can eat it, so can animals. This does not mean that infinite amounts of X will agree with all animals' tummies, so be sensible, but I do not know of anything in the veg garden that's poisonous to them and not to us.
Oh yes, what kind of critters?! Rabbits, chickens, ducks???
Are you not putting pesticides on your produce?
I specifically planted spinach for my ducks mostly and some for me... I also am planting additional tomatoes for the chickens. No reason I need 20 tomato plants alone! So 2 of the cherry tomato plants are just snacks for them.
I've been warned about such things as potato peels being bad for Chickens. However, you need to do research on any plant you'll have be referencing it to the animal you are actually talking about.
Thank you both! We are planning on getting chickens at some point in the near future (this year or next) and we curently have (you geussed it) Llama's (whose manure is jelly bean shaped ie, Llama beans) We won't use pesticides unless we have a problem or my SO does it without my knowledge.