SciAm has a nice report on a survey of people's trust of authority figures. On a scale of one to five, with five being the most trustworthy, they were asked who would provide accurate information on a range of scientific issues. Look at these results: scientists are highly regarded, while religious authorities are deeply distrusted.
Before you get too happy about this, though, check out the source of the survey: this was taken of readers of Nature and Scientific American. Can you say sampling bias, boys and girls? That's disappointing; I'd rather see how the general public views these authorities, since we can already assume that fans of science would rate scientists most highly. It's rather like posting a poll about the greatest musician of the age on a Justin Bieber fan site…you couldn't really rely on the results for much of anything.
I notice that the views of scientists on evolution get the highest trust scores, and I can explain that. No matter what you hear from church pulpits, evolution is settled science — any debate on that matter has been resolved for almost a century. This is entirely why the evolution 'debate' today is so hot and furious, because it takes remarkable ignorance and fanaticism to disagree with it anymore. It's also the case that of all the topics listed, evolution actually has the oldest, most firmly established answer among the bunch, so yes, informed people are comfortable with the views of pro-evolution scientists. It's only the denialists who have to be crazy.
The rest of the article discusses more details of international views on various issues, and mostly they are positive. Just keep in mind — these data are from a well-educated and science-friendly audience, and probably aren't representative of the citizenry as a whole.