While it may be tempting to skimp on the spacing of your vegetables it will greatly impact the yield of your vegetable garden. If spacing is too tight the vegetables will compete too much for light, water, and nutrients, causing them to struggle to grow.
The Three Sisters
This term refers to squash, pole beans, and corn. These three vegetables are ideally suited to be planted in the same space in your garden. The corn begins to grow, the beans climb the corn stalks and use it for support, and then the squash grows in and keeps weeds from growing.
Several types of vegetables can cross pollinate and lead to bland vegetables if they are planted too closely together in your vegetable garden. Two examples are super-sweet corn vs ornamental or starchy corn and sweet bell peppers vs hot chili peppers. Most seed packets will let you know the proper distance needed, though many times in the home garden planting at opposite ends of your vegetable garden will be sufficient.
One thing to keep in mind is that different plants grow to different heights. Make sure you determine how tall your plants will grow and then be sure to plant them so the taller ones are on the north side, this will minimize the amount of light they block.