Discussions have pretty much totally stopped in the Forum, so unless there will be some new activity in the Topic here, this will be the final update on the situation.
I updated the list and have redone it in a new way: New Tags have been added and games are listed according to Genre.

Here is the Canon:
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New Additions:

Jump 'n Runs

[Confirmed]
Super Mario Bros (NES) : This was the first platformer to have scrolling. (Count_Zero)

Super Mario 64: The concept of a 3d platformer was relatively alien at the time yet this worked so well first time out. (garrfunkel)
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First Person Shooter

[Confirmed]
Half Life Series: Since the very beginning the people at Valve have been pushing the boundaries of interactive narrative with the Half Life series. On top of that the controls are perfect and the graphics have always been cutting edge. (DaedHead8)

[Questionable]
Bioshock: The game that proved you don't need multiplayer to sell millions in the internet era. A beautiful combination of innovative gameplay and masterful story telling, this game deserves to be a part of the video game canon. (DaedHead8)

[Proposed]
System Shock 2 - Need more opinions on this!

Deus Ex - Need more opinions on this!

Castle Wolfenstein 3D - Need more opinions on this!
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Action/Adventure

[Confirmed]
Metroid: Extremely good combination of action gameplay, both in terms of platforming and shooting, in an action framework (massive world to explore). (Count_Zero)

The Legend of Zelda: Similar reason, a fairly simple - at first glance - quest game, with a massive world (for the NES) to explore, but with fairly simple and accessible gameplay. (Count_Zero)

Metal Gear series: All of them really but most importantly the first Metal Gear game and Metal Gear Solid. Both of which were responsible for creating and popularising stealth gameplay. (dmgi)

Ocarina of Time: One of the few retro series to jump into 3d so well and adapt so quickly. (garrfunkel)

Tomb Raider: this was the break through game in the mid-90s. I can't think of any other video game character that was on the cover of non-videogame magazines. (Ali D)

[Questionable]
Shadow of the Colossus: One of the most moving stories in a game ever. Massively expansive landscape and every fight is a boss fight. (garrfunkel and DaedHead8)

GTA 3: The staple of sandbox games and the point of comparison ever since (How many times have you heard the words GTA-Clone in the past few years?). Sure other games had done it before, but nothing like what GTA had to offer. (dmgi)

[Proposed]
Ace Attorney Series – Need more opinions on this!

Silent Hill - Need more opinions on this!

Monkey Island Series - Need more opinions on this! Specify which one.
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Casual
[Confirmed]
Wii Sports: Like it or not it is something that completely defines what the Wii is and will always be remembered. (garrfunkel)
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Puzzle
[Confirmed]
Tetris: It pretty much single-handedly popularized the Game Boy (and more importantly, portable gaming in general). (Clyde and Badstar)

Braid: A masterpiece in every sense of the word. (DaedHead8)

[Proposed]
Portal – No Reason given yet.

Katamary Damacy - Need more opinions on this!
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RPG
[Confirmed]
Fallout: It was different and innovative for its time, doing brand new things that heavily, heavily influenced the RPG genre. (Angra)

[Proposed]
Final Fantasy Series – Specify which ones and why!

Seiken Densetsu - Need more opinions on this!

Diablo - Need more opinions on this!

Ultima 4 - Need more opinions on this!

Pokémon - Which one? Need more opinions on this!
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Fighting Games
[Confirmed]
Street Fighter 2: fighting games came of age here. (Ali D)
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Music and Rhytm Games
[Proposed]
Rock Band – No Reason given yet.

Dance Dance Revolution - Need more opinions on this!

[Refused]
Guitar Hero
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RTS
[Proposed]
StarCraft - Need more opinions on this!
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MMORPG
[Proposed]
World of Warcraft - Need more opinions on this!

Everquest - Need more opinions on this!
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Simulation
[Confirmed]
Elite: the first successful space simulator. Everything from Wing Commander, to Freespace, to X3, to Eve Online comes from Elite. (Count_Zero)

[Proposed]
Hidden Agenda: Need more opinions on this!
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Beat 'em up
[Questionable]
Double Dragon: for jump-starting (if not starting outright) the genre of the side-scrolling beat-em-up/brawler. (Count_Zero)
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Shmup
[Proposed]
Ikaruga - Need more opinions on this! (Call Topher Cantler!!!)
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(The descriptions can appear slightly edited)

As you can see, it has grown quite a bit, but many titles are not confirmed yet, because there weren't any reasons given in order to include them. Other titles would also need some discussions.
I'd like to thank everyone who worked on the list. Feel free to participate in the discussions.