Just gonna add my two cents and say that as much as I love Mother 3, as much as it makes my heart churn with all the feels, as much as it is definitely my primary fandom (as if I needed to tell anybody that), I do not consider Mother 3 the best video game ever made.
This is mostly because I don’t think there is a best video game ever made. I’m of the school of thought that as good or beautiful, even, as anything is, video game or otherwise, it cannot be perfect. There can be no perfect video game.
Now, I love all the games that transgendlr posted. A lot, actually. To an uncharacteristically large extent. I have feels for an extremely huge amount of amazing things, including video games, but I by no means can call any of them “the best video game." None of these games - and, in my opinion, no game ever made or ever to be made - can combine all the elements of game design perfectly. Depending on the various, near-infinite factors that go in to game design, some aspects of a game will be emphasized over others, and the game will be imbalanced.
Even Mother 3, which I will never pass up the chance to praise, has flaws. For example, some in-game tutorials come either too late or never at all, which can confuse first-time players, and the jump in difficulty between chapters three and four is unexpectedly large, which as a consequence leads to the latter end of chapter four being far more challenging than it probably should be. In this case, Mother 3 overemphasized story over difficulty curve.
Phoenix Wright occasionally takes unreasonable leaps in logic, or spells things out too easily as if distrusting of its own players to make connections. Ghost Trick limits the paths you can take and ways to solve puzzles to usually a singular solution despite the implied endless possibility of ghost tricks (a limit of the game engine - you can’t program infinite possibilities - and reflects the game’s linear plot. I would like to clarify however that "linear plot” does not equal “bad plot”), and similarly does not translate many of the elements of the game’s high concept very well to a playable form.
These factors don’t make them bad games. Not in the slightest. But even amazing games have things to nitpick at. Theoretically, the “best video game” would be uncritiquable. It would also be the death of video games, so hey.
Just like any other art form, video games have people working behind the scenes to make them, and they will prioritize certain elements of their craft. Just as an Impressionist may sacrifice tiny details for dynamic lighting, so does a video game designer have to make choices in what parts of their game are most important.
Of course, you don’t need to look at this pessimistically: if there can be no best video game, then video games can only improve. And there will always be games that focus on the same aspects as games that you like. And everybody will have their favorite games. You can like something even if it isn’t perfect.
Not to mention the whole different genres and subgenres and game type thing. Mother 3 is a very different game from Portal 2, which is a very different game from Professor Layton and the Curious Village. That doesn’t make any of these games superior or inferior to the others. Why get so hung up on which game is better or worse than another when you can like all of them for their own special reasons?
As far as the actual argument goes, personal opinions are awesome and I love them (I have so many it’s not even funny, as you can see), but I don’t think you can objectively say a video game is the best out of any selection of video games for exactly the reason that everybody will have their opinions. So lets all be opinionated internet game buddies, okay? :3