I usually don't ever see a reason to use the Master Ball, even when dealing with extremely low odds. Most of the time, I just leave it up to chance, so it usually sits in my bag forever. I thought about using it on Wishcast, or however you spell that Pokemon's name, once as a joke, but I always forget to grab the master ball before catching one.
In some old games I used them on some Legendary pokemon just to avoid long captures. In the recent ones, like Violet, I have saved it. I dunno why, it's not much use just being in my inventory, but I don't know which pokemon I can use it on.