Cheating a bit and say Ace Attorney. They did release on the GBA in Japan but over here it was introduced on the DS. It awoke my love for adventure games that I lost sometime when SCUMM was still being developed for.
Heavy on text and low on gameplay elements it is more of a visual novel then the adventure games of old. But the satisfaction of figuring stuff out is still there. The music is fantastic, the characters charming and the stories (for the most part) compelling.
Another adventure game on the DS might not be much of a franchise with only two releases and one not even officially in the US. Hotel Dusk. Its fantastic art style of hand drawn characters is almost unique in the gaming world.
Previously named Uncharted and The Last of Us is up there as well. Bought a PS3 just to be able to play The Last of Us and found Uncharted when I looked up other games from the same developer. Made it worth every penny for the PS3.
It is a bit hard to determine where PC games land when it comes to generations but 2009 falls under that gen, and even if it is popular to hate on it I gotta through a bone to League of Legends. Being free to play it made multiplay with friends easy and it spawned a few games in different genres under the same flag. It is not one of my favorite games, but the number of hours of fun it provided grants it a mention.