In an attempt to counter the increasing cuts to funding for basic research, the Association of American Universities has a neat website illustrating the societal benefits of research. Check out the amusing AAU's Scientific Enquirer, Vol.1, January 2011 link (it's a PDF file) - it tells the story of the screwworm.
In 1955, a $250,000 grant was awarded to researcher E.F. Knipling to study the sex life of the parasitic screwworm. Senator William Proxmire (a Democrat) later awarded this study - The Sexual Behavior of the Screw-Worm Fly - his infamous "Golden Fleece" award which was given to projects he believed were a ridiculous waste of taxpayer dollars. Proxmire, whose degree was in Business Administration, turned out to be rather poor judge of biological research projects since this project is estimated to have had a payback measured in the billions of dollars.
Screwworms were a major cattle parasite in the southern U.S. and Mexico. Knipling developed the sterile insect release technique (take an bunch of male insects, sterilize them, and release them into the wild) which is now used for the control of many different insect species. By 1966, the U.S. was declared screwworm free. The program is estimated to have saved $20 billion for U.S. cattle producers and $7 billion for Mexicans. It's estimated that beef prices are 5% lower because of the eradication of this cattle parasite. In 1992, Knipling won the World Food Prize since his research had such a positive effect on the world food supply. Even Proxmire later admitted he was wrong about this study.
Now, nobody's claiming that all research is this useful to society. Sometimes research contributes just a tiny piece of our overall body of knowledge. But as those pieces build up, we learn more about how the world works and this always has benefits to society, even if they're many years away. It's also important to let scientists decide which research is worthy of being funded, not lawyers and business people (which describes virtually all politicians). You wouldn't necessarily place a PhD scientist in charge of a Fortune 500 company or into a courtroom to argue a case, why the hell would you take a lawyer or CPA and ask them to decide if a scientific research project is worthy of funding?
National Science Foundation (NSF) grants are highly competitive (as well as other federal grants such as those award by the National Institutes of Health, Department of Energy, etc.). Researchers spend months putting together proposals (I applied once in grad school so I'm familiar with the process) which then are evaluated by panels of scientist reviewers. Most proposals are not funded (there's just not enough money to go around). The ones that are funded are serious research proposals judged by multiple researchers in the field to have scientific merit. It's not a perfect system but it's the best we have.
Here's a good example of why I think some politicians are dumb as stumps (or, more likely, mendacious sociopaths) - listen to Jindal's ignorant comment on so-called "volcano monitoring":
Hey Bobby, since you represent Louisiana, how about we cut funding for so-called "hurricane monitoring". Those are federal funds too, you dumb fuck.