The first level of the castle stages begins in an open space a few meters from the entrance.  Mega Man scales the obstacles in his way and begins climbing the side of the building.  Near the top of his climb, he enters the structure and fights the Mecha Dragon.  However, take note of the pipes in the background of this area (seen below in the following screenshots from NES Maps):

I like to think those are the chilled water pipes that service the entire facility.  After fighting the dragon, Mega Man moves on to the second stage which is packed with these massive fans all throughout the level.

Could this be the castle's HVAC system?  Certainly a building as gigantic as Skull Castle requires a large air handling system of some sort, and Mega Man is moving through the ductwork in this level.  Onward to the third stage, we find more pipes and some disgusting, brackish water that has to be the castle's sewage treatment system.

By the time Mega Man reaches the fourth stage, he's inside the castle proper where the utilities are out of sight.  He's fully infiltrated the hideout by now and has taken out several major utilities in the process.  The single-room stage that leads to the rematches with the game's eight Robot Masters is the castle server room with its large screens and heavy placement of sophisticated technology.

Finally, Mega Man arrives underground through the secret acid-lined escape tunnel to close out the game.  It's an ingenious design that shows how realistic the castle could be unlike future designs which make seemingly no consideration for utilities or general infrastructure.  I don't know if Mega Man 2's designers consciously designed the castle with these elements in mind, but they work just the same.  It's a nice touch to a classic game and makes Dr. Wily's headquarters a little more real.