Yes, I know it's a stupid idea. Yes, I'm fully aware of how much it screws up your Hall of Fame and PC, AND YES, I KNOW I COULD HAVE USED IT ON MEWTWO INSTEAD!
*sigh* I have no idea why I thought it was a good idea to use my only Master Ball on a glitch Pokemon back then... <_<
And this glitch Pokemon could have duplicated your Master Ball, too. =P
I used my first one on a Fearow in Blue. I had caught Zapdos and Articuno, killed Moltres (I had gotten through Victory Road the first time and didn't want to go back), and found Fearow. I thought it was Ho-Oh (from the first episode of the anime) and figured that it was in the wild because you encounter it randomly. It was the fourth legendary bird!
I never encountered Mewtwo in game for years, so it wasn't much of a loss at the time.
I believe the first thing that I tried to catch with my Master Ball was (get ready to laugh) Sabrina's Alakazam. Yep.
I was young and inexperienced, and had kind of forgotten about the fact that you can't really catch another trainer's pokemon. I remember thinking, "Wow like that Alakazam is sooo powerful, I want it!!"
The worst part is, that was the fight that I actually managed to beat her before said Alakazam stuck it's spoons where the sun didn't shine. Being young and inexperienced, I didn't realize that it might be a good idea to reload my save from right before the fight.
I came to regret this by the time I got to Mewtwo.