Just like animals in an environment, plants compete for the resources they need in the given space. In your garden, if there is not enough space between plants then resources like nutrients, water and light are squeezed out or over consumed and the plants can suffer. Improper spacing can lead to slow plant growth, low yields and overall reduced plant health. The importance of plant spacing should be stressed especially in monocrop beds.
Not all plants are the same, some actually prefer a little crowding (like arugula, peas and onions). Often, however, the competition compromises the garden’s health. You can make use of this real estate between plants with companion plants that don’t compete for the same resources. Planting shade tolerant plants under broad leafy plants that like full sun makes use of the space intelligently. Consider options for companion plants when thinking about your overall plant spacing and always keep in mind which resources each plant needs.
Below are examples of common garden plants and the recommended spacing for each.
Beets – 1 foot
Broccoli, cauliflower, cabbage and kale – 4 feet
Carrots – 1 foot
Corn – 3 feet
Cucumbers – 5-6 feet
Lettuce – 2 feet
Peas – can be planted thickly
Peppers – 3 feet
Potatoes – 18 inches
Spinach – 1 foot
Squash – 8-10 feet
Tomatoes – give the roots the same amount of width as the leaves take above ground. Determinate varieties will need less room than indeterminates.
In my personal garden, I often plant much more densely than this especially with lettuce, kale, and carrots. I’ve had good luck with higher density planting but I also practice cut-and-come-again harvesting/pruning to maintain a manageable plant size.
For an extended list with more spacing options you can also check out this article from Gardening Know How.