Best memory in RED must be first time beating Elite 4. I was a noobie, so all my Pokémon died almost instantly. But, Hitmonlee of all the pokémon out there saved the day! One High-Jump Kick OHKO Dragonite and also killed Blue's Blastoise! Good days. Also i love that i captured all legendaries (except Mew) the same day.
Today i captured the last Pokémon's so i have all 151. Too soon to call it a memory, but it will be.