I don't really have a particular order, but here's my Top 5:
1. Super Smash Bros. Melee (GC) - One of my favorite competitive games of all time; grew up with the original and moved on to SSBM and it easily makes the list. Just a great, fun game.
2. Pokémon White 2 (DS) - It's Pokémon, and despite growing up with Pokémon Red, Crystal and Emerald, I just find myself loving this generation the most for whatever reason. I still love the earlier generations, but there's just something about B2W2 that I just love overall.
3. Legend of Zelda: Skyward Sword (Wii) - Being one of my favorite series of all time, I had to include this game. I picked Skyward Sword over Ocarina of Time because I feel it's just overall a much more polished game. The character dialogue/relationships, gameplay, and design just feel so much more... Alive.
4. Final Fantasy VII (PlayStation) - One of the few games I actually played and enjoyed on my PlayStation, and it was a hell of a game. The characters and storyline are among the best I've played even to this date, and the vastness of the world just amazed me.
5. Animal Crossing: City Folk (Wii) - An odd pick, but this is - hands down - my favorite game of all time for nostalgia purposes. The soundtrack is so relaxing, and although every character was two-dimensional, they were lovable. From catching extremely rare bugs/fish to the weekly/monthly events, this game was absolutely incredible for just letting go.