"Companion planting in gardening and agriculture is the planting of different crops in proximity for pest control, pollination, providing habitat for beneficial creatures, maximizing use of space, and to otherwise increase crop productivity."
~ Wikipedia

Basil: Improves the flavor and growth of Tomatoes
Repels: Flies, Mosquitoes, Carrot Fly, Asparagus Beetles, and White Fly
Plant With: Tomatoes, Asparagus
Do Not Plant Near: Rue

Borage: Great for attracting bees and more than 100 beneficial insects.
Repels: Tomato Hornworm and Cabbage Worms
Plant With: Tomatoes, Squash, & Strawberries

Catnip: Plant in borders, Cats love
Repels: Ants, Flea Beetles, Aphids, Japanese Beetles, Squash Bugs, Weevils, Cabbage Looper, Cockroaches, & Mice

Chives: Carrots will grow better and improve in flavor
Repels: Carrot fly, Japanese Beetle, and aphids
Plant With: Carrots, Broccoli, Cauliflower, Parsley, & Tomatoes
Do Not Plant Near: Beans & Peas

Chamomile: Improves flavor of cabbage and onions.  Attracts hoverflies and wasps.
Plant With: Cabbage & Onions

Chervil: Radishes grow better and increase in flavor
Plant With: Radishes

Coriander: Enhances flavor of many vegetables
Repels: Aphids, Spider Mites, & Potato Beetles
Plant With: Radishes, Peppers

Dill: Cabbage will grow stronger. Swallowtail butterfly caterpillars eat Dill.
Repels: Aphids, Squash Bugs, Spider Mites, Cabbage Looper, Tomato Hornworm
Plant With: Cabbage, Broccoli, Cauliflower, Corn, Cucumber, Lettuce, Onion,
Do Not Plant Near: Carrots, Sage & Tomatoes

Eucalyptus:
Repels: Aphids, Cabbage Looper, & Potato Beetle

Fennel: Attracts beneficial insects that are looking for nectar, but can inhibit the growth of many plants, so plant away from the garden.
Repels: Aphids, Slugs, & Snails.

Hyssop:
Repels: Cabbage Moths
Do Not Plant Near: Radishes

Lavender: Used for ages as sachets to keep moths from clothing.
Repels: Moths, Fleas, Flies, Mosquitoes

Lemon Balm: Rub the leaves on your skin to repel mosquitoes
Repels: Mosquitoes, Squash Bugs
Plant With: Squash

Marjoram: Improves the flavor and increases the vigor of all vegetables
Mint: Improves the health of cabbage and tomatoes.
Repels: Cabbage Moth
Plant With: Cabbage, Tomatoes

Parsley: Parsley gone to seed will attract parasitic wasps, which are very beneficial. Also a favorite of the Swallowtail butterfly.
Repels: Asparagus Beetles
Plant With: Tomatoes, Corn, and Asparagus

Peppermint: Attracts bees and other beneficial insects
Repels: Aphids, Cabbage Looper, Flea Beetles, Squash Bugs, Whiteflies, & the Small White
Plant With: Cabbage, Kohlrabi, Broccoli, and Kale
Do Not Plant Near: Parsley or Chamomile

Rosemary:
Repels: Cabbage moth, Bean Beetles, and Carrot Flies
Plant With: Beans, Cabbage, Carrots, and Sage

Rue:
Repels: Japanese Beetles
Plant With: Roses and Raspberries
Do Not Plant Near:  Basil

Sage:
Repels: Cabbage Moth, Beetles, & Carrot Flies.
Plant With: Broccoli, Cauliflower, Rosemary, Cabbage, & Carrots
Do Not Plant Near: Cucumber

Summer Savory:
Repels: Cabbage Moth & Bean Beetles
Plant With: Beans & Onions

Tarragon: Good companion to most plants

Tansy: Makes an excellent herb near a compost heap. Attracts Honeybees to the garden.
Repels: Japanese Beetles, Striped Cucumber Beetle, Squash Bugs, Sugar Ants, Mice, Fleas & Moths
Plant With: Beans, Cucumbers, Squash, Corn, Roses, Raspberries, Peppers, Cabbage, & Potato

Thyme: Attracts beneficial insects
Repels: Cabbage Worms, Carrot Flies
Plant With: Chives, Onion, Parsley, Asparagus, Marigold, Nasturtium, Carrots & Lima Beans

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