Oh, yeah, it is fun.
As for the series, the main game has you in the role of a Pokemon trainer who wants to be the world's Greatest Pokemon Trainer. You catch and train Pokemon to take on other trainers and Gym Leaders to make it into the Elite Four. Along the way, you have to foil criminals who use Pokemon for crimes (like Team Rocket) and fight your Rival, who changes each game.
There are also sub-games. The Pokemon Mystery Dungeon game is set in an alternate world where you are a Pokemon that was once human. You team up with another Pokemon of your choosing to go on quests as a rescue team (in the first series) or an Exploration Team (in the DS games.) You have to do a quiz before a new game to see which Pokemon you play as.
Pokemon Ranger is another sub-game and is really cool. You play as a Ranger in regions not covered in the main series. You use the Stylus to capture Pokemon, and you can use them to clear obstacles on the World Map, or to help you capture other wild Pokemon.
Other Pokemon games include the Pokemon Stadium games on the Nintendo 64, where you transfer Pokemon from the original Game Boy games to use on the game, and the upcoming Poke Park Wii: Pikachu's Adventure, where you play as Pikachu and save a land.