From Pew Research Poll: http://www.pewglobal.org/2012/06/13/global-opinion...
Favorable perceptions of America are mostly higher under Obama than they were under Bush 08. Favorability in Europe is significantly higher. Germany (+21), Spain (+25), Italy (+21), and France (+27). The Middle East hasn't changed that much, as would be expected considering our policies towards them. One that is notably lower is of course Pakistan, due to our drone campaign as well as other things such as unilateral assassinations on their soil.
Our drone campaign is seen very negatively. 17 of the 20 nations surveyed have a majority negative opinion of it (even Europe who has a mostly positive opinion of us). Views are strongly unfavorably in the Middle East. Egypt's opinion of it is 89 percent unfavorable and only 6 percent favorable. Obama deserves much of the responsibility for our drone campaign. And personally I agree it is a terrible foreign policy decision, and yet I suspect that is one part of his foreign policy that conservatives don't mind.
When specifically compared to Bush, people have far more confidence in Obama (even in the Middle East). Germany (+73), France (+73), Egypt (+18), Mexico (+26), Japan (+49). The change in Japan is in large part from our assistance with the 2011 Earthquake and Tsunami, which I thought Obama handled very well.
All of our soft power metrics have gone up as well. Our culture, ways of doing business, our idea of democracy, and our science and technology have all trended more favorable under Obama.
And when you look at all of the things that people are dissappointed about in regards to Obama it is that he hasn't addressed Global Warming, has acted too unilaterally, and used too much hard power. Those are the things that people don't like. Those are the things for which we lose respect, and yet those are all the things the GOP argues we should do more of to gain respect.
Opinion of us has gone up by doing the exact opposite of the GOP and we need to go even further from their naive, dismissive and ignorant worldview.