A rough guide to spacing when you're planting out.
Asparagus 14 inches

Beets 6 inches

Broccoli 18 inches

Brussel Sprouts 18 inches

Beans 8 inches

Cabbages 18 inches for smaller types, 2 feet for large

Carrot 3-4 inches

Celery 10 inches

Collards 12 inches

Cauliflower 18-24 inches

Corn 12 inch spacing (plant this in a block for adequate pollination)

Cucumbers 6 inches then thin to 1 foot apart along trellis (one row)

Garlic 6 inches

Kale 12-18 inches depending on type

Leeks 8 inches

Lettuce 10 inches

Onion 6-8 inches between plants

Parsnip 6 inches

Peas 3 inches (assuming planting along a trellis in single row)

Peppers 18 inches

Potatoes 12 inches. You still want about 18inches to 2 feet between rows so you have enough dirt to pile on the plants as they grow.

Radishes 4 -8 inches depending on type.

Sweet Potatoes 12 inches allow 18 inches in between rows.

Tomatoes 24-36 inches

Turnips 4-8 inches depending on type