This is not an argument for the space shuttle. It can be plausibly argued that with manned and unmanned single-use rockets, we could have achieved everything the space shuttle has achieved for cheaper. This is an argument for why we should push manned space flight.

First I will give counterarguments, then arguments.

1. Danger. The first thing to note is that "dangerous" is of little importance while we have volunteers. At the moment, the number of people willing to engage in space flight exceeds the number of people able to engage in space flight by at least an order of magnitude.
2. Expense. Manned space flight is very expensive right now. Contrary to some beliefs, this is not inherent to the process of manned space flight. So far, the expensive part of manned space flight is not the weight of astronauts and the equipment necessary to keep them alive. The expensive part is the design requirement of capability to return to earth. However, this design requirement is not inherently expensive because it implies the possibility of a fully reusable system. As a reusable system, the space shuttle is a failure, but this does not imply that all reusable systems are failures. There have been many designs by many people which could plausibly be engineered into a fully reusable system. It is also somewhat obvious that expense can be dramatically reduced when you realize that fuel costs are a small fraction of the current cost of rocket-based flight.
3. Little return. What is meant by little return is "little return for the money invested". Since manned space flight is not inherently expensive, as it has been so far, the rate of return on the investment in space flight could dramatically change, given a cheaper system.

Now, why should we engage in manned space flight?

1. Motivation. Like it or not, we live in a world where people are motivated by manned space flight. If we remove this motivation, less will be accomplished because people will be less motivated. It is difficult to measure the dollar-worth of motivation, but it is significant. Without manned space flight as a goal, I would expect NASAs budget to be cut by a large fraction.
2. Research. Little in the way of space-based research has yet been accomplished, but that is quite possibly due to the extremely limited times and resources available in space. With a large number of researchers with proper equipment in space for a year or two each, I expect that significant research can and will be done. If nothing else, studying the behavior of materials in space should be a lot easier than on the earth. In addition, there is some hope that new materials can be made in space.
3. War. We have never had war in space, but if war comes, it would be nice to have the upper hand. One important question is: are humans helpful to war in space? The answer at the moment is possibly yes. Currently computers have a very limited ability to plan and cope with unforeseen events. They will cease functioning if they fall out of communication and they are possibly even prone to subversion. Humans are much more adept at coping with unforeseen and inimical conditions.
4. Applications. If manned space flight can be made routine, cheap, and easy, suborbital flights might become routine cheap and easy. How much would you pay for a ticket to Australia on a one hour flight? There is almost certainly a large market for suborbital flights, if we can make the cost and danger sufficiently minimal.
5. Capability. There is some difficult to assess value inherent in having a capability. The ability to send men into space is inherently valuable, just like any other capability. Some unforeseen problem might arise requiring men in space. While this value is difficult to assess, it should not be ignored.