Some people do essentially sit on their bums, intentionally doing little or nothing to seek work, but these folk run the risk (perhaps small) that they'll be asked at some point to provide proof of their job hunting. One can expect to pay hefty fines if unemployment fraud is discovered.
The one-a-week requirement might not seem like much, but if you are, say, an unemployed archaeologist, you might have to scrape hard just to find one open position to shoot for if the economy's bad. And for those who genuinely do want work but who are falling prey to hopelessness and depression after months of rejections, the one-a-week requirement at least keeps them going through the motions.
Applying for unemployment does feel like you're going on the dole, but many argue that it is fundamentally different from welfare. Here in the U.S., regular unemployment benefits (more on that shortly) are paid for by the taxes your previous employer paid. You don't get benefits if you quit, or if your company can prove that they had a good reason for firing you; you get benefits if they let you go due to lack of work or other reasons beyond your control.
Thus, unemployment compensation is designed as a safety net for employees who did nothing to deserve their joblessness. While this might seem like socialist big-government interference to some people, we don't live in a Randian utopia of companies run by ethical, intelligent capitalists. We live in a world where company presidents run their corporations into the ground for the sake of their own greed, leaving scores of hardworking folks (and some slackers too, of course) unemployed. Any ethical government would seek to keep these people from losing their homes and starving, if for no other reason than to prevent national revolt.
And it's not like you can really live on unemployment; you usually get a check equal to half your regular weekly salary. Most of us can't last through a 50% reduction in income for long, but it's better than nothing.
How The System Works in the U.S.
Regular unemployment benefits last for 26 weeks (6 months) and are administered by the states; thus, the precise regulations will vary. The funds for these benefits come from corporate taxes. So, if you're applying for unemployment, don't fear that you're somehow taking money away from someone more worthy or needy than you are -- you're getting money that's coming out of the pocket of the company that laid you off. The benefits are your right; by all means, take them.
Your eligibility is partially based on how much you made; if your paycheck was too paltry, you might be out in the cold. But if your rate of pay was high enough (above or equal to the amount someone would get working full-time at minimum wage), even if you were working part-time, you could still qualify. Your eligibility is also based on how long you worked; if you didn't work a whole year before you got laid off, you won't get full benefits.
You'll have to make a sworn statement every week that you are applying for work as required. You'll have to report income like part-time work or retirement pay, and these sources of income will lower your unemployment benefits. In the old days, you and everybody else had to personally visit the unemployment office every week and stand in line for an afternoon to make your statement. These days, you can often just fill out a form to mail in, or file over the phone. In some states, you may never have to visit the unemployment office in person unless you report an irregularity that you'll have to explain.
If you exhaust your 26 weeks, the federal government currently offers 13 weeks of extended benefits. These extended benefits must be approved every year, and thus their duration can vary (or go away entirely) depending on how bad Congress thinks the situation is.
There are other special unemployment benefits out there. If, for instance, you lost your job when your company moved to cheaper digs in Mexico, you're eligible for special NAFTA benefits. You're also eligible for other monies if you're disabled.