In my experience some of the first people to go are the ones who don't seem to do anything, the ones that clock in at 9, clock out at 5 and stick to themselves all day. The ones who no-one knows what they do or why they do it, sometimes your perceived value has more of an affect than your actual value.
So the easy solution is to be more visible, a big project is coming up? Volunteer to help out!
This both gets you more visible and also provides tangible value to the company, both helping them avoid needing to do lay-offs and helping to make sure you don't go first!
Avoid the blame game
You aren't going to make any friends by getting into a problem and immediately yelling "Joe did it!". Focus instead on helping to fix the underlying issues that caused Joe to do such a thing. Patching up faults and being a team player are important in developing vital relationships that could one day pull you out of trouble.
Be one step ahead
Ok so maybe something new has just been released in your field, maybe something that could be of importance or use to your company. This is the perfect opportunity for you to learn it before its needed so you have vital skills that your company can utilize! This both increases your worth and provides more value to your company, reducing the need for lay-offs in the first place.
Go above and beyond
Find out whats important to your boss, or your bosses boss!, and go out of your way to meet their expectations. Don't overwork yourself, but if you really want to be seen as a valuable person who they couldn't survive without then make sure you are really giving it your all!
Work on core projects that are vital to your companies success! If you work on peripheral projects you too will be seen as peripheral, the best way to be seen as core to the company is to work on its core money makers!
Either way all these suggestions are designed to either increase your worth to the company or to at least increase your perceived worth to the company. Maintaining both is important in ensuring you aren't the first for the chopping block.
Most suggestions even have the advantage of making it easier to get more work if you do get laid off, which is a nice side effect!