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There are other examples of molecules beside water than can do autoprotolysis due to them being amphiprotic. Examples include ammonia, acetic acid, and H2SO4. These aren't really significant; the autoprotolysis of water is the important one you have to know for acid/base equilibria.
The only other significant autoprolysis examples I could think of are 2NH3 (ammonia) forming NH2- and NH4+ as well as 2CH3COOH (acetic acid) forming CH3COO- and CH3COOH2+. In both examples, a hydrogen atom is removed from one molecule and given to the other same molecule. In the examples however, ammonia would be a basic solution and acetic acid would be an acidic solution.
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