Becoming indispensable may be a necessity in this job market, but taking a different approach to your job can change the perception of your position that will last well beyond the recession. You may even find that your job title doesn't really suit you anymore, because you've outgrown it on your quest to becoming indispensable. Not sure where I'm going with this?
Let's say you start out as an assistant, doing thorough work and achieving what's expected of someone in your position. As you've taken on additional responsibilities — some that show your ability to be flexible and some that show off your smarts — you've actually molded your own job description into something that is much different than when you began.
Jobs are typically more rewarding once you've made yourself indispensable; it's nice to know an employer needs you just as much as you need them.