Gary Oak (or Blue) is your character's nemesis through the game Pokemon: Red and Blue. (Spoiler alert!) He always seems to advance slightly faster, is highly competitive and arrogant, and just generally makes himself a constant thorn in the player's side throughout the entire game. He's a jerk, though the lingering possibility that your player might have actually killed one of his Pokemon has haunted players for nearly two decades … and made them feel a bit guilty.
Unfortunately, this one doesn't have a solid answer, and things certainly do look grim. You do encounter Gary on the SS Anne, where you fight him and he again brings out his by now trademark Raticate. After you defeat him, the next time you see him is in Lavender Town. Yes, the "where you learn Pokemon actually die" town. You fight, and his Raticate is nowhere to be seen.
However, there is also a pretty strong case to be made that you didn't kill the poor thing. One, Gary never mentions it. Every other Pokemon master you encounter in the Lavender Town tower mentions their dead Pokemon by name, whereas Gary mentions that he is there to capture a Ghost Pokemon. Also, Raticate just isn't a Pokemon you throw around much in later levels. It's a good early-game Pokemon, but quickly plateaus in capabilities and becomes less desirable as you encounter higher-level monsters.
Hopefully with that knowledge you can rest easier, you (probably not) Pokemon-murderer.