Pokémon Red and Blue
In 1998 I got a blue Game Boy Color and a copy of Pokémon Blue for Christmas; this started an interesting ride through the franchise. Pokémon Blue wasn't my first run-in with the franchise, it was in a local Target where I saw an advertisement in a copy of Disney Adventures where there were a plethora of Pokémon under a gigantic net. The first one to catch my eye was Pidgeot which made me interested in the game because it was "an awesome bird".
I obtained all 151 Pokémon in the Kanto Pokédex legitimately. This is the only time I have ever completed the National Dex.
Pokémon Gold and Silver
Pokémon Mystery Dungeon: Red Rescue Team
Pokémon Diamond and Pearl
Pokémon Mystery Dungeon: Explorers of Time
Even though this is another game from the fourth generation, it deserves a special mention in the Pokémon history part of my user page. After my decent experience with Red Rescue Team, I decided I might as well buy the sequel, Pokémon Mystery Dungeon: Explorers of Time. I heard about it about a week before release and bought it on a whim. On April 20, 2008 after coming home I started to play it... 17 hours later I put my Nintendo DS down to go to sleep. I loved the story and game play so much that Pokémon became a borderline obsession for a few months afterward.
After completing the main story six times, it has gone down as my favorite game of all time. Early in 2009 I found a new copy of Pokémon Mystery Dungeon: Blue Rescue Team so I could finally have the real cartridge for Explorers of Time's predecessor.