This is by no means a complete list, just a few things to start you off.
Blue Cheese - the mold in it is toxic to rats
Green Bananas - inhibits starch-digesting enzymes
Green Potato Skin and Eyes - contain solanine, a toxin
Licorice - suspected to cause neurological poisoning in a rat
Orange Juice - forbidden for male rats only, the d-limonene in the skin oil can cause cancer.
Raw Artichokes - inhibits protein digestion
Raw Bulk Tofu or Meat- can contain bacteria, packaged raw tofu is safe
Raw Dry Beans or Peanuts - contains antinutrients that destroy vitamin A and enzymes needed to digest protein and starches and causes red blood cells to clump
Raw Red Cabbage and Brussel Sprouts - contains antinutrient that destroys thiamin (cooked is fine)
Raw Sweet Potato - contains compounds that form cyanide in the stomach (cooked is fine and a hit with most rats)
Rhubarb - contains high levels of oxalates
Sticky foods such as Peanut Butter, some Candy, and Dried Fruits - poses a choking hazard. Peanut butter can be "cut" with jam or honey to make it more liquid, and reduce the possibility of choking.
Seaweed - the seaweed the comes on sushi or in soup poses a choking hazard.
Wild Insects - can carry internal parasites and diseases
Here are a few that you can give them, but not too much or it may cause problems.
Carbonated beverages. Rats can't burp, so drinking them can cause discomfort.
Dried corn. Contains fungus known to cause cancer in rats, so limit the amount you give them. Some fresh corn is ok in moderation.