In alphabetical order... (I'll leave out the fruit trees)
Asparagus (dislikes) - Onions, garlic
Beans (dislikes) - Onions, garlic, fennel, gladioli, sunflowers
Beans, climbing (dislikes) - beetroot, onions
Beetroot (dislikes) - Climbing Beans
Bell peppers (dislikes) - NOTHING!
Cabbage and Broccoli (dislikes) - Rue, Dill, Strawberries, Climbing Beans
Carrots (dislikes) Dill, Celery
Cauliflower (dislikes) - Strawberries
Celery (dislikes) - Carrots
Cucumbers (dislikes) - Aromatic herbs and potatoes
Eggplant (dislikes) - NOTHING!
Kohlrabi (dislikes) - Beans, Tomatoes
Leeks (dislikes) - Beans, Peas
Lettuce (dislikes) - NOTHING!
Onions (dislikes) - Beans, Peas, Asparagus, Gladioli
Parsley (dislikes) - NOTHING!
Parsnips (dislikes) - Carrots, Celery, Cabbage
Peas (dislikes) - Onion family, Beans, Gladioli
Potatoes (dislikes) - Pumpkin, squash, cucumbers, tomatoes, raspberries
Pumpkin (dislikes) - Potatoes
Radish (dislikes) - Hyssop
Squash (dislikes) - Potatoes
Silverbeet (dislikes) - NOTHING
Spinach (dislikes) - NOTHING
Strawberries (dislikes) - NOTHING
Sweet Corn (dislikes) - Cabbage
Tomatoes (dislikes) - Sweet Corn, Potatoes, Rosemary
Basically the disliked plant if grown in proximity can reduce the yield of the other plant. (From the Australian Organic Gardening Handbook). There is also a list of good companion plants.