The spacing for rows is wider so that you can walk/hoe/weed/etc between them. That spacing is only used for row planting, not for raised bed and sq ft gardening. I do raised beds and I plant my broccoli, for example, 12" in all directions. I ignore row spacing.

I don't cultivate or walk on my gardens and all my veggies are planted in offset blocks, or completely randomly.
I consider traditional row recommendations to be about ease of access for mechanical cultivation and harvest.

The width of rows are for ease of access and so the plants growing there will not steal nutrients form other plants. Those widths are based on "conventional" gardening theories developed since the 1950's and may not mean much in an organic garden or a Square Foot Garden.

sunfrog: it appears to me that the wide rows are for people to walk down. The result is compaction, especially for those who like a "clan" garden, and nullifies their annual attempts to loosen the soil. The more productive answer is narrow beds (say 4' wide) with permanent footpaths (say 1 1/2' wide) between them. Thus, plants can be sown in blocks rather than rows, which are approachable from both sides without anny soil compaction by treading.

The trick is to learn how much space each plant needs around it. I plant onions with 6" space all around each -- imagine lots of rows with each staggered versus its neighbours. This way I can pack 200 onions in a 12 1/2' by 4' bed. John Jeavons taught us that this is in fact more productive than rows, and has diagrams that exhibit this in his book. Regards, Peter.

sunfrog; You are to be applauded. I gardened for years as a row cropper before I caught on. And to tell you the truth most of my gardening friends still row crop. I think it is the influence of the extensive farming methods and power equipment that drives it. I now intensive garden so beds are the normal way for me, and plant spacing is mostly to square foot recommendations. I also do some short row (Elliot Colman) style beds.

Curt

Some crops lend themselves well to rows...sweetpotatoes, tomatoes, and corn. Others lend themselves well to blocks. I use both rows and beds...so do what you want that works for your garden

all stated above is right. do watch though... some seed sowing spacing is smaller and meant to be transplanted later to wider spaces. also, wide rows are partly a way to give whole rows of the same plant more ground to draw from, because the same plants need the same nutrients and quickly drain soil. intercropping helps close up beds and maximise space utility while not over draining soil.

sunfrog: further to your note: potatoes do call for rows, because they need to be hilled. This is done best in rows, whether by machine or by hand. But I would suggest that potatoes need 12' spacing in the row, and any closer wouldn't increase yields enough to be economic. My general rule (oft honored in the breach as well as the observance) is to space so that the leaves of the mature plant just touch each other, and so avoid undue competition for light. Peas need support, so they lend themselves to rows also. Regards, Peter.

If one were to go back and look at gardens of earlier eras, for example at Plimoth Plantation or even the Hermitage in Nashville, one would find that the kitchen gardens back then were planted in blocks and not the long row gardens many people use today. Since it was the housewife of those days that grew the foods eaten in the house and since she was more concerned about efficient use of space a block (or a Square Foot Garden) made more sense. It was not until the husband took over the garden that the long row garden became common, emulate the farmer with this humungous garden and waste space, time, and energy while tending it.

Well, kimmsr, don't forget, if you plant more densely and the crops do indeed yield more, you will pull more out of the soil and then will need to return more to the soil.

One more thought on this perhaps water might have something to do with it . When I was a lad all our water was hauled by hand and wider spacing may have been an advantage for natural rainfall or plant access. Dust mulching was the norm in my area so a couple of days after a rain we were out in the garden with a hoe breaking up the soil so capillary action would not dry out the sub soil. Plants that required watering were kept close to the house and well. (hand pump).

Curt

wayne, don't forget that if you follow good organic practices and maintain your soil in a good, healthy condition it will support denser planting and higher yields with fewer of the problems that "conventional" gardeners experience.

kimmsr, is right about the old gardens before tractor. Large fields on large plantations were in rows so the mule could get to the crops with a plow.
General/President George Washington had a personal kitchen garden that only he worked. It was beautiful & orderly. If I could remember where I saw that pic., oh maybe next time.

Thanks for all the replies everyone!
What a helpful community! :D