There are so many ways to companion plant as you point out. Here are three groupings I look at: (1) botanical, (2) feeding groups, and (3) "better-togehter". I rotate through the beds using the final (3)"better-together" groupings with some seasonal variations for weather.

1. Botanical families (similar cultural needs and pest problems):
* Aster family: chicory, endive, lettuce, sunflowers--usually in cool weather or shade in summer.
* Cabbage family: broccoli, brussels sprouts, cabbage, collards, kale, radishes, turnips-- heavy feeders.
* Carrot family: carrot, celery, dill, fennel, parsley--coole weather, but some like heat.
* Corn (grass family): heavy feeder, lots of water.
* Legumes: beans, peas: nitrogen fixers.
* Onion family: asparagus, chives, garlic, leeks, onions: light feeders, onion maggots.
* Beets and spinach and chard: coole weather.
* Squash family: cucumbers, melons, pumpkins, squahs: warm weather, common insects and disease problems.
* Tomatoes and friends: eggplant, peppers, potatoes: heat-lovers, similar soil.

2. Feeding groups (similar soil and nutrition needs):
* Heavy feeders: celery, corn, cucumbers, eggplant, melons, peppers, pumpkins, squash, tomaotes.
* Moderate feeders: broccoli, brussels sprouts, cabbage, cauliflower, chard, Chinese cabbage, kale, lettuce and greens, parsley, spinach.
* Light feeders: beets, carrots, garlic, leeks, onions, potaotes, radishes, turnips.
* Soil builders: beans, peas.

3. Better-together groups (anecdotal helpmates):
* Potatoes and beans planted together with calendulas, cosmos, daisies, dill, rosemany. Three-year rotation.
* Squash family members, corn, and pole beans planted together with borage, dill, nasturtiums, sunflowers.
Three-year rotation.
* Tomato and warm-fruiters, peppers, eggplants planted with basil, cosmos, parsley, Queen-Anne's-lace. Four-year rotation.
* Cabbage family, lettuce and root crops planted together with asters, calendulas, chamomile, chrysanthemums, cosmos, marigolds, rosemary, sage, thyme. Three-year rotation.
* Roots and greens--carrots, onions, greens planted with caraway, chamomile, dill, fennel, Iceland poppies, asters. Two-year rotation.
* Perennial crops--asparagus, horseradish, strawberries, rhubarb surrounded by borage, sweet alyssum, chives, bee balm, chamomile, thyme, tansy, yarrow, cosmos, dill.

Here is a link that might be useful: HarvestToTable.com

First of all I'm wondering if rotating crops should be done entirely based on families of plants.

First is the question of rotation at all. Many can't or don't - ever. If you know for a fact that you have one of the few purely soil borne diseases then it can be beneficial but don't assume it is mandatory for some reason.

But if you can and elect to then by feeding groups (as Steve defined it) is more common. Some even go so far as to NOT plant by family intentionally since they are prone to same pests and diseases. Further, the most productive use of the space you have available is the most important consideration when it comes to planting schematics and trying to over-plan rotation details interferes with that rule. Real gardens, once established, seldom resemble all the planning that went on paper in the preseason. ;)

it seems futile to rotate these groups

You got it.

am I wrong in thinking that Brassicas, grains, and Cucurbitaceae crops are in most need of rotation.

That isn't my experience. Solanaceae rank first.

are the soil and nutrition requirements for plants in the same families generally very similar?

Degree of similarity is purely coincidental. ;) Soil tilth, drainage, nutrition both types and application times, and watering needs differ and so do required soil temps.

Dave

Thanks for the info guys. Does the Fabaceae family usually have any soil born pest problems? Is it OK to plant peas and beans everywhere to improve the soil?