It's a lifelong thing.
I've always played the games!
Silver was the first videogame I bought for my GBC, but I've been playing since the days of Red and Blue. My childhood was mostly spent at friends' houses playing Stadium or Snap, and my preteens were filled with the 3rd Gen. I stopped for a time around the 4th gen, but it managed to hook me back in a few years ago.
I own a load of the spinoff games, too. Including a Pokémon Mini, Trozei, two Mystery Dungeon games and R/S Pinball. If the GBC games didn't have the battery fail, I'd go hunting for the TGC game, the original Pinball and Puzzle Challenge too. Been thinking about getting a Ranger game.
So, nostalgia is a big factor, of course. Of my 18 years of age, 14-15 of them have been influenced by Pokémon.
It also appeals to my creative side - it fuels my imagination, gives me inspiration, and helps block out the stresses of daily life. The Pokémon are all unique, what with their differing natures and personalities, so there's plenty of potential characters waiting to be created. They're also fun to draw, and some of the games are
gorgeous. I can spend hours looking at PMD: Explorers of Time.
I'm starting to look a little at the inner mechanics, too. Stuff like catch rates, experience gains, you know. Seeing as I've got this love for the games, it makes sense if I use them as research for a potential career in videogame creation.