While it is famous in popular culture, I don't think that there are any useful phenomena other than fission/fusion that can be explained through this equation. In fact, this equation on its own is quite useless (and not used that much either -- it lets one know that mass and energy are not distinct quantities, but after that there's not much you can do with this; $E^2=p^2c^2+m^2c^4$ is more useful).
Besides, nuclear fission and fusion aren't really consequences of just this equation. They are consequences of the underlying theory (special relativity) as a whole. However, they can be easily explained via this equation. Similarly, matter-antimatter annihilation can be explained with this equation, but it certainly wasn't discovered from it.
To put this question in perspective, compare with "What developments came from the equation $F=ma$?". Developments came from the underlying theory of Newtonian Mechanics, but there isn't really anything that comes specifically from $F=ma$.