Depends on which game.
Red: Missingno. In all seriousness. Then again, I'm doing a challenge on that game, in which I go through the game with mostly a Missingno. Unfortunately, I've come to realize that it's just a Bulbasaur with Missingno's look and moveset, but I still don't mind.
Crystal: An Alakazam and a Poliwrath. I caught an Abra near Goldenrod City (sheer luck, of course), and it got me through most of the game as a Kadabra until I was ready to trade it between two of my games to get it to evolve into an Alakazam. The Poliwrath, meanwhile, I had caught early on in the game, and it helped me out a lot as a Poliwhirl until I could get my hands on a Water Stone.
Ruby: Gyarados. It started out as a level five Magikarp I had hatched on Fire Red and traded over, so it leveled quickly until it became one of the most powerful Pokemon on my team.
Fire Red: I managed to catch an Electabuzz in the Power Plant, just because I wanted to train it to see what it was like. Naturally, it helped me get through the rest of the game with no problem, pwning trainers left and right.
Sapphire: It's a tie between my Gardevoir and my Medicham. Partway through the game, I realized that my particular Kirlia that I had been raising since the beginning of the game didn't have the right nature that I needed, so I went back and hunted around near Oldale until I managed to catch the male Ralts that I quickly trained to be the keystone of my team (what with Calm Mind, Thunderbolt, and Psychic). Medicham, meanwhile, was put on my team on recommendation of a friend, and since, it's been my key physical force, getting the Pokemon that Gardevoir couldn't get.
