This is sort of my Top 10. I'm implementing a franchise rule to keep it more varied. In any case, for the most part the other games in the series I view as just as good, but I slightly prefer the one on the list:
10. Team Fortress 2
I spent so much time with this game, and I regret none of it. It's an absurdly fun, well balanced shooter that actually has a personality that makes it stand out from the crowd. It also manages to balance the line between casual and hardcore quite well by being accessible to newcomers, but having enough depth to reward long-term players. The constant additions and updates have only made a great product stellar. And now it's free, so there's really no excuse to not play it save for not having the time.
9. Batman: Arkham City
The amazing thing about this game is that if you strip away all Batman related skins, it's just a well designed game with great combat and fantastic stealth. This is basically what I wanted the Assassin's Creed games to feel like. Arkham City one ups its predecessor by offering more freedom to roam around and by having a better story overall. I really respect that they actually took the chance they did in the final few minutes. Few game series would dare do that. It's just the best adaptation of another character from another medium into game form.
8. Donkey Kong Country 2: Diddy Kong's Quest
All of the Donkey Kong Country games are stellar platformers, but my personal pick is the second one. It carried over the same super tight controls, and the great level design and basically added to it. Dixie Kong was a great playable character. The secrets were more fleshed out. The soundtrack is probably the best in the series. It has a wonderful pirate motif. It's all platforming bliss.
7. Paper Mario: The Thousand Year Door
My favourite RPG. Granted, it's not my go-to genre, but it's probably because this iteration does away with what I don't like about them. The turn-based combat has more agency via blocking/countering attacks, and the seemingly simple numbers of damage mean that attacks are more predictable meaning strategy is more important. It's a game that looks simple but has a crazy ton of depth under the surface. Granted, nearly all Mario RPGs are guilty of this. What makes me give the nod to this though is that the story actually was it's own thing. It's rare to see a story in a Mario game that isn't bound by the series' tropes, but they go all out here and do whatever they want and the result is all the better for it. Despite being a funny game, it actually manages to be serious when it needs to.
6. Banjo-Tooie
I loved the Rare platformers of yore, and to me Banjo-Tooie was the pinnacle of the 3D platformer. I love the 3D Mario games and all, but those tend to be for the most part pretty linear. I prefer the formula that Rare refined by just dropping you in a great big world, and having you explore it, figure out problems and collect various goodies. While Banjo-Kazooie has more charm then its sequel, I put Tooie here because I just think it has such ingeniously clever level design. It's one of those rare sequels that builds on the other in terms of scope and difficulty.
5. Bioshock Infinte
I think the first Bioshock approaches greatness, but has a few flaws that hold it back. The combat never felt right, and the story loses a lot after it keeps going after the famous Andrew Ryan scene. Infinite fixes most every issue I had with the original. The story is much better paced for one thing, and I was constantly driven to find out what would happen next. The gameplay was great with the weapons sounding right and the aim being precise and the vigors dishing out appropriate fireworks. I really like the freedom they give you with open spaces on how to approach a combat situation. Apart from that, I've never connected more to two game characters than I have with Booker and Elizabeth. While people have complained about its politics, the game was never about that. It was about Booker and Elizabeth and the choices they've made, and how one particular choice could affect so much. It has the most ambitious, and best ending I've seen in a long while in any medium.
4. The Legend of Zelda: Twilight Princess
Wind Waker was my introduction to the Zelda series too, and it's still one of my favourites. But, I've got to give the nod to Twilight Princess. Part of it was due to hype. This was a game I was looking forward to for a long time. Mainly because this was the one that made me feel like I was on a grand epic journey. This was done before gritty reboots were too common, but for the time, it felt like a serious upgrade in terms of drama and mood. It just hammered the sense of stakes for me when dealing with Hyrule's inhabitants. It also just has possibly the best dungeon design in series history. Some dismiss Twilight Princess as fan service, but I argue that if all fan service was this good, no one would think that'd be an insult.
3. Portal 2
I love Valve games, and the fact that this beats out Half-Life 2, Team Fortress 2, Left 4 Dead 2; all of which I love, just speaks volumes about how damn fine a game Portal 2 is. I liked the original Portal a lot, but I do think it was too short, and that there was more room to expand on this great game mechanic. Portal 2 does that and then some by throwing in new physics devices, a more engaging story [I was physically shaken after the first third when a certain character surprises you], and it even throws in a great co-op mode too. On top of all that amazingness, it released a robust puzzle editor, so there's an endless stream of new content to go through. Portal 2 is as close to a perfect game I think I've ever played.
2. Metroid Prime 3: Corruption
I still go back and forth on whether I like this, or the original Prime more. Ultimately, I'm going with this one for a few reasons. I dug the original Prime, but it wasn't until I played Prime 2 that, when exploring the Sanctuary Fortress that it all clicked. I got the essence of Metroid, and I just let it wash over me, and it was glorious. Prime 2 is also almost as good, but regrettably features a few key design flaws. Prime 3 meanwhile takes everything that came before it and makes it sing. The level design is wonderful and they manage to solve backtracking issues by using the gunship. The worlds are all imaginative and detailed and feel like real places. The controls are the best use of the Wii remote's unique features. Pointing to aim and shoot is far better than dual joystick, an it really immersed me along with the other uses. The hyper mode adds an intriguing mechanic, and the story really does increase the stakes. It's a perfect end to the best trilogy in video games.
1. Super Mario World
This was the first game I ever played, and it's still my favourite. It's the culmination of all the Mario platformers and refining it to their best. It's music is perfect, it's visuals are perfect, it's controls are perfect, it's sense of freedom in a 2D platformer is unparalleled, and it's a deep, rich game that hasn't aged a bit. Super Mario World is a game I would want my future kids to play.