How many space missions are exploring our solar system right now?

The number is 27!

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CC-BY-SA Olaf Frohn

Right now there are 27 different missions ongoing to explore our solar system. A high number for something that is not part of our daily news cycle. Those missions currently concentrate on the sun, mars, mercury, venus, the earth moon and some asteriods.

Source: http://www.raumfahrer.net/news/raumfahrt/01052013213936.shtml