What are some molecules stable in outer space that are unstable under terrestrial conditions? What are some molecules stable in outer space that are unstable under terrestrial conditions?
So there are many molecules that violently react on Earth because they're too charged, have unfilled valence electrons, or have extra electrons in their outer shells. But in space, they often can't really "find" another molecule to transfer/attract electrons - in a long period of time
 A: Well, neutral hydrogen (HI) would be the obvious example since it is very common in space but not seen on Earth,except that HI is a single atom, not a molecule. Then we can go to OH, the hydroxyl radical, that does very nicely in emission nebulae, but is highly unstable on Earth.Then there is carbon monoxide, CO, which only lasts a few months on Earth. Ammonia, NH3, exists in space, but doesn't last long on Earth.
On the other hand, H2, molecular hydrogen, is stable in both, as is H2O.
A: Another interesting one is trihydrogen, H3+, which forms when molecular hydrogen is ionized to H2+, then via 

H2+ + H2 → H3+ + H

it's not stable in terrestrial conditions, but is found in interstellar space and in the planetary magnetospheres, although it can be studied in laboratory conditions in plasma discharges (indeed it was first detected in the laboratory by J.J. Thompson in the early 20th century, it wasn't detected in interstellar space until 1980). 
As well as being the simplest triatomic molecule, it's very important in the chemistry of the interstellar medium via proton-transfer reactions, e.g.

H3+ + CO → HCO+ + H2

or 

H3+ + O → OH+ + H2

which are building blocks for the more complex molecules seen in space. 
