How much watering a plant requires depends on a number of such as; type of soil, rainfall, the effect of wind, the amount of organic material in the soil, whether mulch has been applied etc.
Different soil types hold different amounts of water, with sandy soils holding the least, and heavy clay soils the most. The more water a soil can hold the less often it will need watering.
A good guide is to try to imagine your plant above ground mirrored by the root system below ground. For example a tall plant or well established plant that has an extensive root system will require less water.
Over watering can have more of a detrimental effect on plants as this may encourage the roots to search in the top few centimetres of the soil only, discouraging roots from searching deeper into the soil.
The requirements for watering vegetables can vary depending on the crop, and growth stage. For example, leafy crops may need regular watering in dry weather, particularly on light soils to encourage leaf growth.
Drought tolerant, once established
Onions, leeks, carrots, beetroot, sprouting broccoli, brussels sprouts, winter cabbage, spring cabbage, winter cauliflower, parsnips, marrows, spinach beet, Jerusalem artichoke, parsnip, radishes, swede, turnips, chicory.
Water after flowering, (only in dry weather) if needed
Peas, beans (runner beans need more water than french beans) and tomatoes
When to water:
Apply directly to the soil either in early morning or evening, when the air and soil are cool (reduces loss to evaporation). Slug susceptible plants (leafy crops etc) should only be watered in the morning though, as slugs are not only nocturnal but will be more active if you wet the soil, thus creating ideal conditions.
Reference GardenOrganic: http://www.gardenorganic.org.uk/todo_now/watering_vegetables.php