Pokémon Red / Blue

Legendary Birds (All Lv. 50)

Articuno-Ice/Flying type found in the Seafoam Islands cave.

Zapdos-Lightning/Flying type found in the Power Plant.

Moltres-Fire/Flying type found in the Victory Road cave.

TO CAPTURE THE LEGENDARY BIRDS...
-Save when you're right next to one at full strength with your Pokémon.
-Once you start battling him, use lesser attacks to weaken him down till his HP is in the red.
-Once his HP is down in the red, start to lower his key stats, like attack and defense along with accuracy.
-Once his stats are shot, then use a Pokémon that knows Thunder Wave, Sleep Powder, Spore, or Stun Spore to get him either paralyzed or asleep.  This further weakens the Pokémon.
-Throw Ultra Balls at it till you finally capture him.  But, with all the damage you've done to it, it won't be long before you have yourself a legendary bird.  
-NOTE:  The same technique can be used to capture Mewtwo, level 70, but it's much easier to use a Master Ball on him rather than the Legendary Birds.