My favorite is Gold. While I liked Red (my first game), it was a little too glitchy for my tastes, and Gold was a lot better in that regard. Gold also added a lot of features I enjoyed (breeding, day/night, etc.), and I loved how it featured both a new region and a return to an old one.
Ultimately, though, my love of Gold probably stems mostly from other factors that affected my gameplay experience. While RBY probably marked the height of the Pokémon series' popularity with the general public, a lot of my friends still played Gold, and I have many fond memories of playing my games with other people at holidays, sleepovers, etc. Gold was also the first time I made a team (when I first played Red, I pretty much just used Blastoise), and the first time I completed my Pokedex. Even though my team was terrible by competitive standards (I had an unevolved Totodile, two other water types (at least one of them wasn't weak to electric, though), a fairly weak flying type, and Pikachu), I enjoyed the experience of raising all of those Pokémon through repeated Elite Four battles and encounters outside Mount Silver. I had more time to play Pokémon then than I did now; consequently, it played a larger role in my daily life, my interactions with friends, etc.
I also had to work for every Pokémon I got; I couldn't just look for Pokémon on the internet or that sort of thing. (Admittedly, there was no internet connectivity until gen 4, so I guess this applies to gens 1-3, but still...). When I wanted an Omanyte, I had to borrow a friend's Yellow (because I didn't want to restart my own gen 1 games, and he didn't care about that file) and play through most of the game to turn my Helix Fossil into a Pokémon. Now, I probably would just ask someone for an Omanyte, or look for one on the GTS. Certainly, online trading has made Pokedex completion more efficient, but there was something rewarding about having to spend many hours just to get one Pokémon. And yes, I recognize that I don't need to trade with people online to complete my Pokedex, but that's not really the point. Going back to the old way of doing things now would just feel tedious, and because I'd know that there was an easier way of getting Pokémon, I would feel like I was wasting my time. But back then, when there was no easy road, so to speak, succeeding in Pokedex completion, getting my team to level 100, etc., felt fantastic.
I've still enjoyed all of the games since Gold, but when I think about the game that played the most influential role in my childhood, Gold is the clear winner. Now, the games seem easy, and the things I work hard for (breeding perfect IVs, EV training, etc.) seem more tedious than genuinely rewarding (particularly as I enjoy training competitive Pokémon, but never actually have time to use any of them outside of in-game). Playing Red and Gold on emulators more recently, I've realized that they're easy, too, and if I were playing them for the first time today, I don't think I would necessarily enjoy them as much as I did 13-14 years ago. Sure, I would still like them, as I play Pokémon more for comfort/relaxation these days than for challenge, but I'm sure they'd seem dated compared with modern entries. But when I put the "nostalgia goggles" on and look at the games in the context of my childhood, nothing beats Gold.