Will multiple lay-offs hurt your job prospects? Yes.
Once when I was involved in hiring someone, I came across a resume where the person had 3 months at this job, 9 months at that job, 6 months at the next, etc. I think the longest he had stayed at one job was a year. And my immediate reaction was, I don't know why he spends so little time at each job, whether he quits because he gets bored easily, he gets fired for incompetence, or what. But whatever the reason, odds are that if we hire him, he's going to be gone in 6 months. This was for a highly technical position where it would take the person months to learn the job, so he probably wouldn't even be productive before he was gone. Not worth it. I tossed the resume in the "no" pile.
The problem is that an employer doesn't know the real reason why you no longer have a certain job. If the company ran into financial problems for reasons that had nothing to do with you and had to lay people off, fine, not your fault, bad luck. But often companies fire people for incompetence but put it down as a layoff as a nice gesture so the employee can collect unemployment insurance and doesn't have a firing on his record. Of course if you were really fired for stealing from the company or physically assaulting a co-worker or some such, that will look bad, too.
In your case this is water under the bridge, you can't take back the layoff's now. The best you can do is to have good but simple explanations ready. WorkerWithoutACause says to describe the first two as "the project came to an end". Assuming that's even halfway true, yes, that sounds way better than "I got laid off". If you have a good explanation that you can sum up in a few words, like "project ended", I'd put that on your resume. I'd have an explanation ready if someone asks in an interview. But unless the interviewer asks for details, I wouldn't get into it too far. It can easily sound like you're making excuses. A simple, "the company got into trouble because of the recession and they had to lay a bunch of people off" is about as much as I would volunteer.
If I were you I would try to make my next (or current) job longer term to make the resume look better. Like if I had three jobs in a row that for whatever reason I stayed less than a year at each, I would try to stay at least 3 or 4 years at the next job. Even if I absolutely hated the job, I'd knuckle down and stick with it for a few years. Then when i felt I finally had been there a respectable amount of time and got a new job maybe I'd have a party, but whatever.
I once had a job that I quit after a month. Shortest time I was ever on a job. Down the road I just left it off my resume. Job before ended in August, next job started in September, I just put month and year on all my job dates so it wasn't clear whether the gap was almost 2 months or a couple of days. No one ever asked. Not saying you can do that exact "trick" here, but sometimes just being creative in how you present things can help. I'm not suggesting lying, I'd never flat out lie on a resume, partly as a matter of principle and partly because it's very bad if and when you are caught. But you don't have to volunteer negative information.