We've already covered how important it is to volunteer for tasks that make your supervisor grind her teeth. While that part of the formula to indispensability is more about them, this part is all about you.
Whether you're new on the job or you've been in the same position for a while, begin asking more questions and opening your ears. Learning as much as possible about your industry will make you a more self-sufficient worker, boost your performance, and polish your attention to detail. Your boss will notice your enthusiastic interest in your job and your intensified knowledge about what's going on around you.
As soon as your company lifts any hiring freeze it has in effect because of the economy, take on the challenge of training someone new. The company will think highly of your willingness to contribute and the confidence in your own abilities won't go unnoticed. You may just become the go-to person for training new people, which gives you a big leg up in becoming indispensable.