I've heard wiggling is good for plants, because it promotes root spreading. Does artificial wiggling do the same thing? if so how much should I wiggle the tree artificially?
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There is an article here http://woodlandsteward.squarespace.com/storage/past-issues/windaffe.htm that discusses the effect of wind on tree growth but not of artificial movement.
Basically different trees respond to wind stress in different ways, and continued movement appears to disrupt the root soil interface so that trees end up shorter, and more stout. If the movement is primarily from one direction, the roots are forced to grow larger on the other, presumably by hormones such as ethylene. So in a forest, the edge trees are smaller then one protected from the wind.
So, there is a cost to the stress of movement, and that is to trunk growth, but it could increase the roots to protect them from winds that might otherwise uproot the trees.
As an aside, if you're growing seedlings inside, some people recommend brushing them as you pass by to simulate wind stimulation enhance root formation.
Would your trees benefit from eg. banging your head on the trunk regularly? Probably not as you might be stimulating unnecessary root growth for the tree's local environment.
You're probably talking about a response to movement of air, or movement by mechanical means, known as thigmomorphogenesis, some technical reading on the subject here
It may be useful to introduce a fan on a low setting into a greenhouse when you're growing seedlings so that there is gentle air movement around them, causing the seedlings to develop thicker stems and shorter growth rather than becoming tall and spindly. It's also useful to stake newly planted trees in a manner which allows for the stem or trunk to respond to wind with a little movement in the upper parts, so that the trunk thickens and becomes stronger as it grows in response to that, although it shouldn't be staked in this fashion in such a windy spot that its roots rock too.
This, though, does not mean trees (or other plants) will necessarily respond well to a good thrashing about or 'wiggling' performed by you or anything else, so I'm in agreement with Graham here - leave 'em alone.