Here's a high-minded top-ten list: "The 10 most pressing philosophical issues of the 21st Century". Let's overlook the somewhat oxymoronic notion of a "pressing" philosophical problem -- any issue that is actually pressing is not going to be waiting on philosophers for a solution. I guess it's somewhat charming that philosophers think they are that important.
Here's the list (more detail at the link):
10. Finding a new basis for common sensibilities and common values.
9. Finding a new basis for social identification.
8. The Mind-Body problem.
7. Can freedom survive the onslaught of science?
6. Information and misinformation in the information age.
5. Intellectual property, in the age of remix culture.
4. New models of collective decision making and collective rationality.
3. What is a person?
2. Humans and the environment.
1. Global Justice.
And here's my breakdown:
10, 9: 1 seem to be essentially the same, or at least closely related. All are driven by globalization, the progressive kniitting-together of disparate cultures by technology and commerce. All seem to center around the nagging contradiction at the heart of liberalism; the idea that there must be a neutral public sphere and people's deepest moral commitments are relegated to private or semi-private space; resulting in the paradox of having to tolerate the intolerant. How do people and communities with different sets of values coexist? Good questions, and I can believe that philosophers have something to contribute here.
8,7: are chestnuts that philosophy has made no progress on in hundreds of years and there is no reason to think that they will do any better in the future. Also, what exactly is pressing about them?
6,5,4: are very interesting and important issues but not very philosophical. They will be dealt with by economists, lawyers, techies, and media designers. The answers will be on the order of "Google PageRank" and "Wikipedia" and "Facebook": new forms of social media, possibly linked to new structures of governance. Philosophy has little to contribute, sorry.
3: Good question, one where I suppose philosophy may be able to say something, because personhood is socially defined, not a biological property. Although I think sociology and science fiction (particularly Phil Dick and Octavia Butler) have done a better job of addressing it.
2: What was the question? Yes, certainly we need to become more cognizant of the environment and our relation to it, but that's a job for scientists and the environmental movement. Not sure what philosophers have to do with it.
Honestly I'm not nearly in touch enough with the actual practice of modern philosophy to judge it. It seems that most branches of philosophy are constructed to explicitly avoid making any progress. I guess I believe that philosophy should be in the business of examining and improving the world's assumptions and abstractions. An obviously important task. But what counts as an improvement? If they are the watchmen of thought, who watches the watchmen?
More anti-philosophy philosophy here.