Applications outside the earth are clearly a good fit for Robots. It is dangerous for humans to get to space, to be in space and to return from there. Unexpected can happen anytime in space.
But to make the Robots operate in Space, there are too many challenges. Due to high Vacuum, many lubricants could not be used, you cannot predict the temperature, the surface will not be smooth to travel, etc.
Though the ultimate Robot to replace the Astronauts is yet to be invented, scientists has already started creating Robots which can partly replace humans in Space. Following are the examples for that..
Robonaught - A humanoid Robot designed by NASA and DARPA, It is designed to have dexterity, range of motion and task capabilities roughly equivalent to that of an astronaut in a space suit. Each arm of this Robot have 150 kind of sensors to sense to perfection.
Sojourner Mobile Robot - This has ultimately explored the surface of Mars. This is more of an R/C car than a robot as it was completely remote controlled from Earth. The pictures it provided from the Martian surface were breath taking.
Mars rover, Curiosity - Curiosity is the most successful Rover. It is an automated motor vehicle that propels itself across the surface of the planet Mars. Rovers have several advantages over stationary lander: they examine more territory, and they can be directed to interesting features, they can place themselves in sunny positions to weather winter months.The primary goal of rovers is to discover the history of water on Mars.
Source: Learn about Robots in Space, Wikipedia