Hi Rex I am not much of a tomatoe grower as they usually get frosted my side of the mountain. however I have read that they grow well near asparagus,celery, parsley, carrots, basil and chives, but they dont like rosemary, potatoes, kohlrabi and fennel. they apparently like to grow in the same area year after year and prefer compost made from their own stalks and leaves. Sowing iron nails in the soil around them is meant to protect them from cut worm, french marigolds nearby from nemotodes and nettles (stinging) deters mould helping tomatoes to keep better. Perhaps you have tried some of these? some things just help but are not a cure all and there is no substitute for soil quality and moisture.
Apparently asparagus, carrot, onion, parsley, basil, garlic, margueite daisy,
Toms give lettuce and silverbeet shade
Toms and cabbage and umbellifere (coriander/ celery/ parsley/carrots - as their insects eat pests of toms)
Well, there's a book called Carrots love Tomatoes, by Louise Riotte... so I guess you could start there.
I find they don't grow well near onions (neither do peppers) but that may just be me, not sure if it's official companion planting lore.
That carrots benefit the growth of tomatoes is mentioned here: http://en.wikipedia.org/wiki/List_of_companion_plants, here http://www.gb0063551.pwp.blueyonder.co.uk/seeog/companion/ and here: http://www.ghorganics.com/page2.html -- with the warning, as you say, that the carrots will be stunted.
Re Sean's comments -- what I'm reading suggests that onions (and other alliums) are supposed to be good for tomatoes. However ... it's all just theory for me right now (I'm writing an assignment on companion planting for an organic horticulture course), although I'm looking forward to testing it out in spring :-)
I'm happy to have found this discussion. Thank you to all those who have contributed.
An American source I found says that geraniums and petunias will act as a trap crop, attracting the beetles away from the tomatoes. I gave up on a heritage tomato last summer that was covered in green shield bugs -- they weakened the plant and ruined the fruit. I figured out that the problem was the site -- right outside Mum's kitchen window, which was never curtained in summer. Those bugs were attracted by the light that streamed out of an evening. The flowers of carrots and parsnip are supposed to attract beneficial insects, which might include ones that prey on those bugs. Nasturtiums the same.
Tansy made into a liquid fertiliser/compost tea is supposed to be great for tomatoes. Same with stinging nettles (you can brew the two together).