Voted Melee just for all the memories I have with that game.
I still enjoy watching high level play of Melee but I like playing Ultimate more.
Halo pretty much single handedly made Xbox relevant in the console market. Not a small feat. I think the second installment is superior but since I don't like any of them the impact factor places the first game above.
In the other section list of games there are multiple once I enjoy very much.
Conker's Bad Fur day is still leading in number of laughs a game have created.
Ico is the first time I played a game that I truly felt was art as much as entertainment.
Luigi's mansion while short and a bit repetitive is still a fun experience. Best played as a sort of arcade game only going for high scores.
Advance wars is one of my favorite series (not including the battalion wars games). The first game is good but I consider each of the sequels to be superior.
Golden sun is one of my favorite RPGs. I really like the puzzle elements of combining Djinns. Bit text-heavy but still enjoyable today and one of the best looking games on the GBA.