There is danger lurking in some seemingly harmless foods that we eat. Familiarize yourself. The safest thing to do is to only feed dog/cat food and treats.

Foods
Alcohol - our pets are much more sensitive to alcohol and should never have access to it.
Apple seeds, leaves stems - contains cyanide.
Avocado
Caffeine
Onions & Garlic - dogs cannot break down compounds in these foods which can lead to red blood cell damage.
Chocolate - can be fatal, particularly the darker chocolates and baker's choclates. Be aware of cocoa mulch used in gardening; if ingested will act like chocolate.
Grapes & Raisins - can be fatal, causing renal failure
Fatty foods - can not only upset the GI system, causing vomiting and diarrhea, but cause pancreatitis and need medical attention.
Persimmon, peach & plum seeds - inside of seeds contain cyanide.
Rhubarb
Moldy Foods - can produce poisonous mycotoxins which can cause serious and/or life threatening conditions. Secure your garbage cans.
Nutmeg
Nuts, especially Macadamia nuts
Xylitol (sugar substitute) - very dangerous - found in foods, toothpaste, sugarless gums, etc. One stick of sugarless gum can be highly toxic to a 20# dog.
Yeast doughs: can rise in the stomach and create alcohols, resulting in alcohol poisoning. The expansion of the dough can cause gastric tortion (twisting the stomach) leading to death.

Plants
There are too many to name - Here is a link to the list. Click "show only toxic to" dogs or cats. This will bring up only the toxic plants.