Ponyta back in R/B/Y. Granted this was long ago, and I have since learned many things. Among them don't waste your Masterball on a Ponyta because your level 80 Blastoise keeps OHKOing them. Instead, switch out for something not horrifically OPed and catch it normally. And that Articuno/Zapdos/Moltres and Mewtwo don't respawn.
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Rayquaza in Ruby, just a few months ago for Dex completion purposes. Outrage, Rest, and being level 70 changed the problem from just having a low catch rate to trying desperately not to get wiped.
I think I eventually brought out the Registeel I had just caught, taught it Protect, and stalled while chucking Timer Balls. It was the only thing that didn't get pureed by Outrage, and only by a little bit. God that sucked.
"...Are you crying?" "Of course not, it's liquid pride. Totally different thing." -Shining Armor
Back in the day, Rayquaza on Ruby version. I spent almost a day dedicated trying to catch it, brought my gameboy everywhere my mother took me. I stopped and never did catch it because I thought it was impossible.
Anyone saying anything other than Chansey in RBY is either wrong or hasn't played Gen I.
I believe I caught Chansey in Unknown Dungeon in Yellow. My hardest catch was Zapdos in Yellow; that was infuriating. Zapdos would either dodge the pokéball, or it would break immediately. It took me many retries and ultra balls to catch it...
Articuno, Moltres, and Mewtwo were quite kinder and didn't give me all the bullcrap Zapdos gave me.
original safari zone Chansey, tauros or khan. followed by rayquaza in emerald. spent a day reseting and trying again, actually found it as a shiny then only to try a pokeball with the first turn and landed it. now I try a pokeball first turn for every legend I find.
The only one that stands out as being extremely hard to catch in particular to me is Rayquaza in Emerald, I remember having difficulties with other legendaries, but for some reason that one is what I remember the most, and it seemed like it took forever until I finally caught it.
"Greater love hath no man than this, that a man lay down his life for his friends. John 15:13"