The 2004 Game of the Year is Half-Life 2.
The runner up is World of Warcraft.
The master thread for all of these contests can be found here.

It's time for a Runoff vote to determine the Game of the Year for 2004.  Three games in the original poll made the cut.  A lot of games were mentioned from "Other" votes, but only one game got more than one vote.  Here are the current choices:

Half-Life 2 (PC)
The sequel to the original Half-Life did not disappoint.  It sold over 12 million copies, received a 96 on Metacritic and won 39 Game of the Year awards. 

World of Warcraft (PC)
During the late 1990’s and early 2000’s many companies were trying to get a piece of the huge cash cow that was the MMORPG industry.  The big ones at the time like EverQuest and Final Fantasy XI had a peak of around 500k subscribers, and FFXI was Square-Enix’s most profitable game up to that point with that level of subscribers.  Then Blizzard comes along with their MMO and blows all of that away.  At its peak World of Warcraft managed to have a mind boggling 12 million subscribers.  It also set a new standard for MMO’s and every MMO game that followed would try to be the “MMO that would kill WoW”.

South Park on WoW:  https://www.youtube.com/watch?v=TBmG7eRjZ2g

Metroid Prime 2: Echoes (GameCube)
The GameCube needed a second Metroid game to make up for the N64 having zero.  This sequel would get a 92 score on Metacritic and sell over 1.1 million copies on the GameCube alone.

Here is the new game added based on "Other" votes:

Paper Mario: The Thousand-Year Door (GameCube)
This whimsical RPG is perhaps the most beloved in the Paper Mario series.  It scored an 89 on Metacritic and sold over 1.9 million copies on the GameCube.

The runoff vote for 2004 Game of the Year will end on Tuesday, Nov 7 at 11:59 PM, EST.

Games that didn't make the cut:

Rome: Total War (PC)
Dragon Quest VIII: Journey of the Cursed King (PS2)
Grand Theft Auto: San Andreas (PS2)
Metal Gear Solid 3: Snake Eater (PS2)
Spider-Man 2 (PS2/XBox/GameCube/PC/Mac/GBA/DS/N-Gage)
Halo 2 (XBox)

I am going to just come out and say that more than 9 games released this year deserve to be in the poll.  Some of the games listed below would have been serious GOTY contenders if they had simply been released one year earlier.  But in the 2004 poll there just isn’t space for them all.  Anyway, here are the other notable games, some of them being very notable:

Cave Story (PC)
City of Heroes (PC/Mac)
Far Cry (PC)
Rollercoaster Tycoon 3 (PC)
The Sims 2 (PC)
Unreal Tournament 2004 (PC/Mac/Linux)
Burnout 3: Takedown (PS2/XBox)
Gran Turismo 4 (PS2)
Katamari Damacy (PS2)
Need For Speed: Underground 2 (PS2)
Ratchet and Clank: Up Your Arsenal (PS2)
Red Dead Revolver (PS2/XBox)
Star Wars: Battlefront (PS2/XBox/PC)
Pikmin 2 (GameCube)
Paper Mario: The Thousand Year Door (GameCube)
Ninja Gaiden (XBox)
Fable (XBox)
Star Wars: Knights of the Old Republic II (XBox)
Tom Clancy’s Splinter Cell: Pandora Tomorrow (PS2/XBox/GameCube/PC/GBA/Mobile)
Fire Emblem: The Sacred Stones (GBA)
Kirby and the Amazing Mirror (GBA)
Mario vs Donkey Kong (GBA)
Metroid: Zero Mission (GBA)
The Legend of Zelda: The Minish Cap (GBA)
Kingdom Hearts: Chains of Memories (GBA)
Warioware: Touched (DS)
Lumines: Puzzle Fusion (PSP)
Ridge Racer (PSP)

Jak 3

Edit: Holy shit, Metroid Zero Mission, KH Chain of Memories and Zelda Minish Cap came out that year too. Man, these four games mean A LOT to me and are some of the few I still enjoy to replay even to this day. I'm gonna still vote for Jak 3, but all of them are terrific games. Sadly, the Jak and Daxter franchise doesn't get too much love these days. Not even by their creators...

Other - Paper Mario: The Thousand Year Door. What a game.

For once, not Other.

5. Fire Emblem: The Sacred Stones: A relatively dark entry (Demonic Monsters roaming the world) with a tower that allows for almost infinite XP if you can afford for the weapons that break. As such, probably the easiest entry in the series.

4. Knights of Honor A medieval RTS where you manage an entire country a bit like the Total War series with some additional mechanics and where the RNG on ressource allocation can make or break a game.

3. Burnout 3 Takedown. The first of the "modern" Burnouts, where crashing the ennemies or tons of traffic is the main goal next to racing. Still very much fun to play to this day.

2. Knights of the Old Republic II: The Sith Lords. Much better than it's predecessor, but sadly never fully finished as LucasArts first gave them more time for new locations and features but then wanted them to Christmas Rush the game. Since the extension was only verbal, they were forced to finish what was working and cut all the unfinished parts, and were not even allowed to bring the rest as an expansion, free or paid.

1. Dragon Quest VIII. The first one to ever come out in Europe and imo still the best in the series. Ragazzo!

GTA San Andreas on PS2 with a lot of cheats is the funniest thing ever!

in my opinion this is the most underrated year in video game history. So many of these titles were absolute classics for me, but aside from that it was also the year that in my opinion PC gaming took a quantum leap forward.

Paper Mario: The Thousand-Year Door. It deserves all the hype it gets.
In a close second is KOTOR II. I've still never played the restored content MOD and still loved the official release both times I've played it.
Spider-Man 2 is a god among movie tie-ins, and still is great as a whole. Admittedly, the Insomniac titles are clearly better.

Paper Mario: The Thousand-Year Door. The best in the series imo.

I'll go with Half-Life 2 here. Good narrative, very strong atmosphere, really well-paced gameplay progression and sense of exploration. Perhaps the most well-crafted FPS ever made.