While technically non-canon, Pokémon Snap was my personal favourite. I can see the craze with the series but I've never been as enthusiastic about its world, especially as I've only seen the movie (which was brilliant) and played a bit of Coliseum.
For those who don't know, Pokémon Snap was the N64 title where players would be on rails taking photographs of different Pokémon in several environments. The whole idea was to get the highest score, and the more awesome the photo, the more points you'd get. It was far more complex than just snapping away at random like a rail shooter (sometimes I wonder if the game was made to parody the genre), and took real patience and eyes for detail. It was quite a slow experience but still a very good first person game, which to this day I'd recommend.
What made it such a good title for me was that it relied on replay value, as you'd have to revisit older levels to rack up more points before unlocking more. It was also quite funny, as a lot of the Pokémon poses were hilarious such as surfing ones, dancing ones and ones performing moves which only made the N64 even more awesome. One of the most criticised issues was that there were only 33 out of (at the time ) 151 Pokémon in the game. Many critics also were concerned about the lifespan and replay value, but I always found myself coming back to this each time I played it.
Probably not the best title based on the adventures of Pokémon Island, but certainly one of the more adorable ones.