In the original Mega Man X, the order you do the stages in matters even more than usual for a Mega Man game. Besides the bosses being weak to each other's weapons, the stages themselves will also change depending on what order you do them in, both automatically and based on you firing weapons. For instance, defeating Storm Eagle will cause his airship to crash into Spark Mandrill's power plant, reducing the number of hazardous sparks in the environment, but also making a room that was formerly dark now pitch-black except when lit up by enemies passing through it. The lava pools and waterfalls in Flame Mammoth's stage can be frozen using Chill Penguin's weapon to allow you to walk over/climb up them without being destroyed.
Worth noting: these changes are almost entirely separate from the boss weapon order, meaning there's a lot more variation in the order to play the stages in even once you know what that order is. You can also replay a completed level at any time to see what's changed, and to use those changes to reach previously unavailable heart containers and upgrade pods, which - to my knowledge - was something you couldn't do in the series before this game.