About 1%.  

Bill Dickens, Bryan’s first economics professor, writing in the Milken Institute Review:

[A] number of estimates suggest that we have paid a price for the extended unemployment benefits adopted by Washington in response to the recession – somewhere between 0.4 and 1.8 percentage points of unemployment. 
Steven Mullins, in Econ Journal Watch, arguing against Barro’s claim in the Wall Street Journal that the extra benefits raised unemployment by 2.7%:

The UI benefit extensions that have occurred between the summer of 2008 and the end of 2010 are estimated to have had a cumulative effect of raising the unemployment rate by .77 to 1.54 percentage points.
Numbers quite similar to Dickens’s take.  Mullins finds that even when you take into account the fact that awful recessions have high unemployment, recessions when UI benefits last longer have even more unemployment.  
Mullins’s short empirical piece is just sophisticated enough to change some skeptical minds, just transparent enough that any macroeconomist can quickly take in the message.  For policy-relevant work, we could use more publications like this.  A good complement to the structural approaches that fill the journals today.  
But here’s the bad news: If we cut unemployment benefits back to the usual 26 weeks, a 1% fall in the unemployment rate wouldn’t cause a 1% rise in the employment rate.  Mullins and Dickens take the same reading of the literature that I do.  Mullins: 
[W]hen their unemployment benefits expire, the majority of the unemployed leave the labor force rather than take a job. 
I know that people game the unemployment system and start looking for work a few weeks before the benefits run out: I know people who do that.  
But that’s not most of the story.  Instead, when your benefits expire, you usually just stop calling yourself “unemployed” when the government bureaucrat calls to survey you.  Instead you just tell her “I’ve stopped looking for work.”  
Generous unemployment benefits change how people answer a government-run survey.  Further evidence that people respond to incentives.  
[Update: When I refer to “%” above, I should be referring to “percentage points.”  xkcd’s take on the %/percentage point distinction here, Drexel Math Forum’s more serious take here.]