On my course they say that for a 2,000 word essay you should aim to write a minimum of 1,800. If you write less than that they will only mark the essay if you show definite signs of achieving a pass mark. There is no specific penalty, but they say it is their experience that under-length essays do not receive good marks.
As far as going over the word limit is concerned, they are fairly strict and say they will not read anything over the word limit. Again, there is no specific penalty, but they will treat your essay as though the last part has not been included, and so you will lose marks for structure as your essay will have no conclusion. However, at the moment we do not have to submit our essays electronically, so generally essays that are 50-60 words over will get away with it.
If you are less than 10% over the word limit, you can generally cut it down a fair bit just by removing unnecessary words and rephasing sentences to make them more concise.
If you're seriously over, go through your essay with a highlighter pen, separating it into sections, for example, introduction, point one, point two, point three, point four, point five, conclusion. Then read through all the points you're making and delete the one which contributes the least to your argument, and is therefore less effective.