A: For crops that we're growing to eat the leaves or roots (lettuce, spinach, carrots, beets, radishes, etc.), no. You could grow just one radish seed, for example, and get one radish (although that wouldn't make much of a dinner).
For crops that you're growing for fruits or seed pods, growing more than one is helpful and even necessary for a few.
Tomatoes and peppers, for example, have "perfect" flowers that include both male and female parts on the same flower. Usually a little bit of wind is enough for those to pollinate themselves.
Other crops have separate male and female flowers and depend more on insects (primarily bees) to pollinate each other. Prime examples are cucumbers, melons, squash and pumpkins.
The more pollen and bees you've got floating around, the better the pollination odds. Cucumbers in particular benefit from having several plants growing near one another. Ditto for corn, which pollinates mostly from wind blowing pollen onto the silks and definitely benefits from having many plants in a block or mass.
If you're growing any of the above plants inside (i.e. in a greenhouse), you'll probably have to pollinate the female parts yourself with a small brush since bees and wind aren't around to do the deed for you.
Besides lack of pollinators and/or wind, three other factors can affect how well your fruiting and seed-pod-forming crops pollinate and produce:
1.) Not enough light.
2.) Extreme temperatures (above 90 degrees and below 55 degrees can harm pollen).
3.) Excess nitrogen in the soil.