The key to being indispensable is the same no matter what the economic situation. It doesn't change. The keys are simple.
Communication / Transparency
Keep everyone in the loop on what you are working on. Go above and beyond the normal communication that may need to happen with your boss about your status report. Instead, post that status somewhere more public that anyone who is interested can see it. If you have the ability to blog about your work internally then do that. If you are a consultant then blog to the world the things that you are doing. Let everyone know everything that you are doing, learning, and deciding. You will be repaid with trust since you are not trying to pull one over on anyone.
Creativity / Ingenuity
Find creative ways to make more money or save money. Find ingenious ways to get your work done faster and save money. The keys may be more automation, or just changing a process. Spend time thinking about how to make everything faster and easier. Solutions that make the company money will keep you in house when layoff happen.
In order to be really great at what you do, you must be committed. That may mean spending more time at work or spending time outside of work improving your skills. Better yourself for the specific job you have, and for additional responsibilities you may need to take on. What things are you not doing today that you may be asked to do next week or next month because someone else had to be let go? Are you ready for those tasks?
In order to be able to communicate everything efficiently and to be creative and even to find the time to learn new things, you must be organized. Everywhere you look you can see people who are well organized that outperform those that are not. It's rare that a disorganized person can reverse this trend. In those cases, they would most likely be able to excel even more if they were organized. Don't let clutter get in the way of what you have to do, and don't miss deadlines because you weren't sure where a request went to. Pick an organization System like Getting Things Done, or Zen To Done, read about it and implement it. Becoming organized will have a positive impact on your performance and output.
Being indispensable is hard. It takes a lot of work and communication.