The whole 'Gary's Raticate died' thing. Several occurrences in the Gen 1 games and their remakes seem to strongly imply this: Gary (Blue)'s Raticate is nowhere to be seen after you battle him on the SS Anne, which possibly means Gary tried to heal his Raticate at a Pokémon Centre, but died of its injuries before he could reach one.
The next time you see Gary, he's at the Pokémon Tower in Lavender Town (cliche, I know...), where he is looking over the Pokémon graves, ostensibly mourning his dead Raticate. He doesn't seem all that upset about it, however - he puts on his usual loudmouth tendencies and sarcastically laughs that your Pokémon don't look dead, before smirking that he can at least faint them.
The incident isn't mentioned for the rest of the game, not even at the Indigo League before you battle him for the Champion title. Maybe Gary didn't really care about his Raticate that much, as it was only a temporary team filler before he comes up with his final roster as a Champion, but any other Trainer would at least show sadness for the departure of their team members.