I dumped mine in the PC, as I already had plenty of water types by that point in the game. In HG, I started with Totodile, and I like Feraligatr better than Gyarados. In SS, I think I had a Quagsire on my team that I wanted to use instead (as I had one of those on my team back in Gold).
In general, I tend to have enough electric weaknesses as it is in-game, between a water-type starter (except in SS) and a flyer, so I tend to shy away from Pokemon later in the game that share that electric weakness. Also, I suppose I tend to feel that shiny Pokemon should be properly EV trained before use, and I wasn't in the mood to EV train the Red Gyarados when I got it, so I dumped it in my PC and figured I'd deal with it later. As it turns out, I still haven't gotten around to training it yet.