As a kid, I just always used it on Mewtwo as I felt it was "his Pokeball" & nobody else's. Only the best for the "most powerful Pokemon"! The only other exception was Mespirit as a teen, because it was just extremely impractical for me to get a team to prevent it from fleeing back then, & I wanted to be done with it so I never had to hunt it again. Everything with Mean Look that I had available was weak to it, & it was driving me nuts. Admittedly I had a bad team at that age, but anyway.
As an adult... I hoard. I don't really like how it looks with the new ball animations in 3D, so I tend to never use it unless it's very comical. I've used it a few times on a shiny Magikarp for example. It's got an M on it, so M for Magikarp, right? There's literally no reason to use it on a shiny like that for me since I always have a False Swipe team now or whatever, but I love people's reactions to seeing it. If I had gotten to that point recently, I would have used my Master Ball on the shiny Zubat I found on my recent replay of SoulSilver & nicknamed her "Mistake" as a personal joke, but sadly it was early game so I only had regular Pokeballs. Really wish I had a Love Ball for her instead. I have a goal to eventually catch a shiny Whiscash in a Master Ball, as W is for Whiscash (says so on his head, /j) & the M on the Master Ball is clearly perfect for him, heehoo.