Twilight Princess
One of my top favourite games of the series. Most of the allure comes from the art style. I absolutely loved the dark and gothic feel of the game as opposed to its WindWaker counter-part. The plot did seem a little cluttered, but I thoroughly enjoyed the game nonetheless. Another thing that contributed my love for the game was the overall epic nature of it. The final boss battle(s) with Ganondorf just reminded me of a remastered version of the final battle in Ocarina of Time with better instrumentals and gameplay; easily my favourite final boss battle out of the Legend of Zelda series. Incredibly epic.
Super Smash Bros Melee
This, along with my third choice, were games that really involved the "multiplayer" aspect of my childhood. Needless to say, I spent a substantial amount of my childhood playing Super Smash Bros on the N64, and when Melee came out I was overjoyed. It's just an overall great game, I mean where else can you brawl against friends with Nintendo characters? This was also my go-to brawler/fighter, with Soul Calibur coming in at a close second.
Other: Final Fantasy Crystal Chronicles
Absolutely loved this game, and the reason I did was due in part to the multiplayer and replayability of the game itself. I spent a lot of time playing this game with my bros as well as with friends, and I enjoyed every minute of it. The whole "team player" aspect of it also drew me in as you did have to rely on your fellow companions a lot.