I quit twice, actually :) .
I was introduced to the franchise when I was eleven, with Pokémon Blue. Loved it, played it like crazy, annoyed my parents so that they would buy me the other versions of essentially the game same... then Gen 2 came out and it was on all over again. By the time Gen 3 arrived, my parents had enough and I was stuck playing on the PC.
The first time I quit was after playing some Gen 3 on an emulator. To be honest, at first, I hated it. I've been told back then that Gen 3 couldn't connect with Gen 2, and not knowing anything about Regional and National Dexes, when I saw Treecko, Torchic and Mudkip in the Pokédex where Bulbasaur, Charmander and Squirtle were supposed to be, I was upset. I thought they completely remade the franchise and threw the old Pokémon out for good (thus, my reaction when I saw Zubat was: "THIS is what they kept?"). I thought the game dragged, with routes being so long and everything... but the final straw, and I know this is petty but I was 15 back then, was a Pokémon design... I quit the game with the intention of never playing it again the moment I saw Lunatone.
A few months later, my friend who gave me the ROMs sent me a save file with the complete national dex and my faith in the franchise was restored :) . Gen 3 slowly grew on me over time, but I was stuck playing with the emulator, so I coudn't experience the social part of it.
The second (and longest) time was when Gen 4 came around. The DS emulators available back then were too slow for me to enjoy the game, and by the time they became fast enough, I stopped caring.
Fast forward to a year and a half ago ("2.5 years ago now" - SaniOKh from the present) when I finished college, got a job, and decided to start a retro videogame collection. After buying some old consoles and games, I got a SNES cart with an internal battery (used for saving games back in the day) about to die, and decided to learn how to replace internal batteries. My first test subject was the good old Pokémon Blue. I managed to replace the battery and then decided to try the Mew Glitch. And after that I just kept playing. When I was done, I replaced the batteries in all other Gen 1 and 2 carts. And then, slowly, I started ordering the games I missed online: Gen 3, Gen 4, the remakes, and even managed to score a DS Lite in a great condition. Ultimately, I bought Gen 5 and a 3DS. So here I am, fully equipped and definitely back and definitely excited about Gen 6.