Forgive me, for it was late and I was tired
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Mining the moon would bring Helium-3. Helium forms in the sun, and transfers through space; cosmic rays some how turn helium into helium 3 (and other forums of helium, like helium 4; don't ask me, I'm no scientist). Helium 3 does not reach Earth, because it is diverted by our magnetic field; rather it reaches other parts of space, such as the Moon. Heating the rocks, soil, dust, and wherever helium 3 may be, releases the helium.
If we learn how to mine the moon for helium 3, which we are researching how to, this may help us reach our journey to Mars and beyond.
As for helium mining for Earth? If we learn how to fuse helium3 this will eliminate complexity of generators; with helium 3, a electric current is yielded by heating, no generator needed; this is said to capture 70% - 88% of the energy in fuels, and used directly as energy (electricity); it also produces far less pollutants.
As for hydrogen in space; it would be easier than on Earth. Take Saturns largest moon: Titan. It is believed that Titan contains materials similar found on Earth that can be extracted to create hydrogen. Extracting may require a - 400degree environment, and the material will already be liquefied on Titan. With organic chemicals on Titan, it could be limitless if we moved in a orderly fashion around it, and obviously not take to much of it. How much, and is it really organic? We will have a space craft out there earlier next year, if everything goes, well to try and find information.
Yeah, Titan is a bit far, so I don't think that helps us much...
yeah, I know! 
