Why do you use the subjunctive after 'quiero que'?

It should be said that it is not always trigged by that construction, since the subjunctive only follows this clause if there is a change in subject (i.e. quiero que tu hagas/usted haga/él haga/ella haga/nosotros hagamos/ustedes hagan/vosotros hagáis/ellos hagan/ellas hagan). That is why, more often than not, you will see the subjunctive after 'quiero que', as you would after 'queremos que', as long as there is a change in subject.