Why don't you plant things equistant (rows and "columns")?

[Pancho]

As title.

Why don't we plant things Xcm apart in rows with rows Xcm apart?

Everything seems to be squished within the row but has lots of growing room between the rows. If you obey seed packet instructions (I don't).

[andygates]

Because most gardeners are simple folk and an equilateral distribution makes their heads explode...

...plus, thinning.  Easier to thin a row than a clump.

[Cyclops]

There has been research that shows by planting things equidistant the leaf canopy can block out light and prevent weeds from growing (obviously this won't work with leeks, onions, etc.)

As Andy says though you sometimes need distinct rows to allow for thinning or earthing up of tatties.

[Si]

as mentioned - rows rather than blocks allows light to get in, allows you to get in to weed/thin/earth up, and, further more, it allows air to get in which reduces the chance of disease.