A question I often wonder about when watering outdoor pots in the dead heat of summer. Should I just make sure the soil in the bed/pot is watered sufficiently, or is it necessary/advisable to also water the leaves and stem? My naivete makes me think that hitting the above ground plant will keep the plant cooler and reflects more of what happens when it rains, but I may be wrong.
If your humidity level inside is too low (often a problem is you run the Heat or AC) then plants do benefit from a misting of water around the plant to try to raise the humidity in that area of the room.
However, mostly you just want to water the soil beneath the plant rather than the whole thing. This is because water sitting on leaves of plants, or excess humidity around them (especially things like tomatoes) can actually lead to disease. It also provides little actual benefit to the plant.
Most places outdoor plants will have plenty of moisture in the air to be just fine. However, if you are in a desert or other very dry climate you may have to mist around your plant so that the humidity around the plant stays at the proper levels.
Although some doubt was cast on it in an earlier question, there is the concept of "scorching". If this occurs (and isn't a myth) then the water droplets on the leaves act as small lenses refracting solar heat and scorching plants. Some plants are effectively immune, but if this does occur, other plants and growing buds might be particularly sensitive.
Another point against foliage watering on outdoor plants, is that the water on the leaves will evaporate more quickly than if it falls on the ground (this is where @wax eagle's humidity comes from). It is therefore wasted. At times of drought you want to get all the water where it needs to be to minimize water usage (and your water bill!).
I agree with the advice already given as regards outdoor plants. However, as pointed out by wax eagle, apart from cacti and succulents, most indoor plants, dislike the dry air produced by central heating in winter (unless you have a humidifier, of course, or they live in the bathroom or the kitchen) and they will suffer - many may not survive - unless you give them the humidity they need. You can create a moist microclimate around them by:
misting the whole plant by spraying it with tepid water - but not in bright sunlight, for the reason given by winwaed, or
placing the pot or, better still, a group of pots, on a layer of pebbles at the bottom of a shallow tray, into which you have poured a little water, just enough to almost cover the pebbles but not to enter the bottom of the pot, or
double-potting - putting one pot inside a larger pot or container, and filling the gap between them with moss which will need to be kept continually damp.
If the leaf tips of your indoor plants turn brown and shrivel, or the leaves wilt, although the plants are being watered sufficiently, this is usually a sign that the plants need more humidity in the air.
As mentioned in other answers already, watering the foliage is mostly a waste of water due to evaporation.
One exception is if you are "fertigating" (fertilizing + irrigating) aka "foliar feeding". This is where you spray a dilute fertilizer mixture on the leaves so that the plant takes up nutrients from the leaves instead of through the soil. But this isn't really watering as much as feeding -- the plant isn't getting all that much water as compared to nutrients.
Most research seems to conclude that watering the leaves themselves has little benefit and can in some instance cause some risk.
Applying specific types of "feed" to the leaves seems to be noted as a separate process and has been shown to be beneficial especially amongst fruiting plants.
One query I have had in regards to the idea however was brought about by watching my garden's reaction to summer rain.
I have wondered if the first small shower on the leaves somehow triggers more effective feeding from the root system as the rain continues to come down.