A Link to the Past was the first thing to come to mind. Of course many games since have done storms much better, but that one had the biggest impact on me personally. The jump from 8 to 16 bits was a hell of a thing!
Reminds me of when the Super Mario All-Stars version of Super Mario Bros 3 added thunder and lightning to the background of the Koopa airships. It may have been the coolest upgrade to the whole vibe of that game.