The Human Element
Despite the abilities of robotic missions to last far longer than manned missions, it's impossible to discredit the abilities of a human being to adapt and change according to the needs of a mission. Whether it's an interesting crater on the other side of a hill on the Moon or the disastrous outcome of a technological or engineering failure, having a human as the tool of the mission can and will prove vital when the opportunity presents itself.
While rovers can go for years without water or food, they can't do close to the amount of work a human can in the same time. It may take months to travel a mile for a rover, but if you get an astronaut and a vehicle on Mars, they can cover an extrememly larger area than any robotic mission.
Obviously, a human has to come back, but this final mission objective is also the best thing about sending a human to do a robot's job. Until very recently, all the robotic missions sent into space have been destined to remain there. Yet, in 1969, when Apollo 11 landed on the Moon, the astronauts brought back handfuls of lunar rocks for scientists to examine and study. Having the ability to not only explore but also retrieve from the mission location makes sending a human on a twelve hour mission just as useful as sending a probe on one that lasts a decade.
As a matter of fact, the early days of spaceflight were dependent entirely upon the abilities of human pilots. While not nearly as famous as the Apollo program which they allowed to happen, the Mercury and Gemini projects were at the forefront of spaceflight, with missions ranging from operational tests to continued record breaking attempts at orbital distance. These projects established the backbone of manned spaceflight which made it possible for Americans to become the first humans to land on the Moon. None of which would have been possible without the use of manned spaceflight.
Finally, the most important aspect of the human element is the capability to solve problems. When Apollo 13 was faced with certain doom, the abilities of the astronauts and engineers to safely and effectively guide the mission back home without any casualties was no doubt one of the best adaptations to any crisis in space flight history. It certainly earned its descriptor: "the most successful failure in NASA history".