Xenoblade, because its the most epic rpg ive played in scope, music, story and soul. It also has has 4 entries since then and it has become the defacto nintendo rpg and its the new final fantasy of jrpgs

Most influential - Minecraft
Personal favourite - Souls
Best - hm...probably Portal

Uncharted.

However I didn’t really like Lost Legacy and 4 overstayed its welcome so it has gotten stale with PS4. I did like Golden Abyss though. The first three games however were great because of their great action and setpieces in imaginative locations and a fun story with likeable characters. There were well thought-out levels with clever puzzles and platforming. They really felt like an ‘adventure’. However the series kind of failed at ‘exploration’. While obviously a linear story-driven game should be linear, the collectables weren’t interesting. The Tomb Raider 2013 series is much better at that; where the collectables have something to do with the location and story and provide back-story to certain events.

I would also include the Wii series. I know it’s not our first choice but I’m sure it was most of the world’s first choice.

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.

Does the Witcher count? We wouldn't have The Witcher 3 if it didn't start with that humble, awkward first game so my vote automatically has to go to The Witcher. If not TLOu, Uncharted, Souls maybe, Dragon age, idk it's hard to choose.

Eh. While the games were new in the 7th gen. IP itself dates back to the books. I guess it counts as a new game IP. Tho 1 sucked. 2 is improved but still a lot of issues mainly the 360 port Just a clunky game to play. Don't think people took to it until 3.

Personally - I’d say Xenoblade.

But I also see Xenoblade as the third iteration of the “Xeno” branding within the Xeno-franchise; branding switches with the move to different parent companies. And in another way, the child franchise of Final Fantasy 6 and Chrono Trigger given the first game began as a sequel to both of those and absorbed and advanced on core elements: Mechs, a divine power source, an alien god who will bring the apocalypse, etc…: Magitek Armour = Gears, Lavos and Goddess Triad = Deus, the source of magic for Espers and Magitek Armour = Slave generators, the day of Lavos = awakening of Deus into Xenogears, and those evolved into successor versions in Xenosaga and Xenoblade. But FF6 and Chrono Trigger were both headed up by Kitase with Takahashi has one of the primary creatives, while Takahashi himself created and ran Xenogears, Xenosaga (well, the first game, the second and third had him pulled off, and they continued from his notes, but went in strange directions), and Xenoblade

Objectively - Wii Sports, it was the biggest killer app of the generation. And for something that was derided by its jealous critics as a “fad” it certainly spawned a lot of successor type games in terms of software collections and motion controls - from Wii, to Switch, to Xbox Kinect and PS3 Move, to VR. Its most recent sequel, Switch Sports, sold 13 million + units, Ring Fit Adventure (the sequel to the spinoff, Wii Fit) has sold over 15 million, 28+ million for two titles making it one of the most successful franchises this generation.

TW1 was terrible indeed and TW2 while better wasn't exactly a flawless gem that TW3 was but it was a start and turned into the greatest IP I can think of in gaming, hell TW3 wasn't flawless when it dropped either and took some patching to get it from exceptional to flawless. I believe The Witcher series has strenthened itself as one of the biggest IP in gaming in the time since the third game released and will sell up there in the top five including Multiplayer games when the next comes out, if it reviews well, unless something rocks the top five list in the mean time. I think of Uncharted and how that didn't really excel, it was good but not great, as with the souls games really iffy and awkward start. So since you make a good point that it isn't new really new IP. I'll go for TLOU, it hit the landing out the gate so well it made people critique the second over the slightest of little flaws. 

1 and 3 are brilliant, 2 is great but I couldn't get into X after about 2 hours (I know it takes longer). Considering even my cousin who is a lot better at games than me spent hours trying to beat the final boss and failed, I don't think I'll ever touch X again until it gets an enhanced remaster or remake with a casual mode. The original Xenoblade on Wii and 2 I played on Normal Mode. Defintive Edition and 3 I played on Casual Mode. 

If Xenoblade Chronicles went on Windows (and for sure PlayStation on top of Nintendo) I guarantee the sales would rival or exceed Final Fantasy.