The cases of most modern computers are designed to play a large part in channeling the air flow through them from the fans and over the parts that need it.
Remove the case the air is no longer channeled to the places it needs to go, those parts start to overheat so the fans get faster and faster to try and cool them down (hence also noisier and noisier)
So in short, if you run your computer without its case firstly it will get noisy, secondly you risk damaging parts due to overheating as they are no longer getting sufficient cooling.