Normally, unemployment insurance is a form of insurance. Employers pay premiums for their employees, and those premiums are used to pay benefits should those employees become unemployed. Both premiums and benefits are based on wages, covering some fraction of income for some limited period of time - typically up to 26 weeks - while the employee finds a new position similar to work he has done in the past. During a recession, the federal government often funds an extension to unemployment benefits on the theory that it takes longer to find a similar new position during a recession.
Sometimes, however, getting a similar position may no longer be realistic. Not as many human market makers are needed when there are computers to help with the job. There will probably never again be as many pre-IPO PR jobs available as there were during the dot com bubble. In these cases, extended unemployment benefits can simply facilitate denial: they'll encourage people to turn down realistic job offers while they hold out for their dream job that no longer exists.
There is data available to quantify this effect. Studies regarding extension of benefits indicate that it causes the average unemployment period to increase by between 4.2 and 10.6 weeks - 8% to 20% of the additional benefit time.
That's why Congress' recent refusal to continue extending unemployment benefits beyond the basic period is likely to be the best jobs creation program of this year. Unemployment benefits had been extended to 99 weeks - nearly two years - and now they will be going back down to the regular 26 week range. Doing the arithmetic, we should expect a reduction in the unemployment rate of about a percentage point - from 9.5% to 8.5% - as the change takes hold.
[edit: Unfortunately, Congress caved and renewed emergency unemployment shortly after this post was written. It was finally allowed to expire at the end of 2013. The first half of 2014 then saw the fastest job growth in over a decade.]
Data and anecdotes on the effect of insurance on unemployment
Another place unemployment benefits go: