How do you approach writing a personal statement?

My biggest critique of personal statements is that they fail in their primary purpose - to be PERSONAL.

3 tips.

Know your audience - if you are applying for varied courses look at the skills and the similarities that underly them. Also make sure to refer to some of the differences so each course feels like it is being addressed specifically.
Know your competition - if you are applying for a course like medicine, know the common things that people do and shift some emphasis on some of the things that you do that are different.
Know your style. For non-medicine personal statements, you can afford to be more lyrical so make it a great piece to read - full of flair and emotion. For medicine, make it more laconic but just as captivating with great stories and explanations.