According to the Angiogenesis Foundation, if you can control the blood vessels forming process called angiogenesis, cancer can't grow. That is because cancer cells need nutrients coming through blood vessels.  If the nutrient supply is blocked, cancer will starve to death.
 
The organization gives out a list of foods that are of anti-angiogenesis. Please note that there is no meat from any animals except some fishes.
 
Right now it is not completely known what foods are more potent than others. 

William W. Li, M.D., President of the Angiogenesis Foundation, discussed a few foods that have potent anti-angiogenesis properties including Bok Choy, Strawberries, Tomato, Artichoke, Flounder on the nationally-aired TV program The Dr. Oz Show.

Fish
 
Flounder (sole)
Haddock
Halibut
Herring
Mackerel
Salmon
Sardines
Tuna 
 
 
Fruits
 
Apples 
Blackberry
Blueberry 
Cherries
Clementines
Cranberries
Grapefruit
Lemon 
Nectarines
Oranges 
Peaches
Pomegranate 
Raspberries 
Red grapes
Strawberries
 
 
Herbs & Spices
 
Basil 
Black pepper
Cinnamon  
Flaxseed 
Garlic
Ginger
Ginseng 
Lavendar
Licorice root 
Nutmeg 
Oregano 
Rosemary
Sesame seed 
Tarragon   
Tumeric
 
 
Legumes
 
Lentils
Lima beans
Soybean
Sword jackbean
Tofu (soft, firm, dried, fried), miso, natto
 
Mushrooms
 
Enoki mushrooms
King oyster mushrooms
Maitake mushrooms
Matsutake mushrooms
Oyster mushrooms
Reishi mushrooms
Shiitake mushrooms
 
 
Nuts
 
Cashews
Chestnut
Pine nuts
Sesame
Walnuts
 
 
Seaweed
 
Arame
Dulse
Kombu
Mozuku
Nori
Wakame
 
 
Shellfish
 
Cuttlefish
Oysters
Sea Cucumber
Shrimp and prawn
Squid and squid ink
 
 
Vegetables
 
Artichokes  
Beets
Bok choy
Broccoli
Brussel sprouts
Cabbage  (red, savoy, white)
Carrots
Cauliflower
Chard
Endives
Kale
Mustard greens
Olives and olive oil
Onions 
Parsley
Parsnip
Peppers 
Pumpkin
Radishes
Salsify
Scallions
Shallots
Soybean sprouts
Spinach 
String beans
Sweet potatoes and yams
Thistle
Tomatoes 
Turnip and their tops
Watercress
Winter squashes
 
 
Other
 
Dark Chocolate
Green Tea
Maple Syrup