NES: Punch Out!! - Addicting arcade goodness while also hard. Hard to top this game when it still holds up to this day.
Game Boy: Donkey Kong 94 - A masterpiece of game and level design. This game shouldn't have any right to be this good, on a system like this no less. Still better than 99% of game released today.
SNES: Donkey Kong Country 2 - The REAL best platformer of the system. It balances gimmicky level design with proper platforming without getting overboard about it like 1. Though, note I'm playing Super Metroid for the first time right now, and I'm really liking what I'm playing.
Game Boy Color: Wario Land 2 - This game is HUGE. So many collectibles and hidden secrets to find. Lots and lots of content for a handheld game.
PS1: Crash Bandicoot 2 - The first game was, well, the first of its kind, but it wasn't executed well. However, this game perfected everything the first game introduced. Some problems aside (very few though), this game really is near-perfect.
Game Boy Advance: So many awesome games...Warioware Inc, Mario vs Donkey Kong, Rhythm Tengoku, Advance Wars, etc but yet I can easily say my favorite of the system is without a doubt, Wario Land 4, which is my favorite game anyway.
PS2: Jak III...I guess? I don't know. For all the praise this console gets it's mostly JRPGs which I hate, and the multiplats were all better on Gamecube so I played them on that. I also don't like the big exclusives, like MGS2 in particular. I still haven't played Ratchet and Clank though, mind you. I need to.
Gamecube: F-Zero GX. The perfect arcade racer.
Nintendo DS: A tie between Rhythm Heaven and Elite Beat Agents, but I'm leaning towards the latter.
Xbox 360: Halo 3. Easy.
PS3: I actually hate most of the exclusives, Uncharted aside. So, Tekken Tag Tournament 2, for being the best Tekken game.
Wii: Punch Out Wii, Zack and Wiki, DKCR, Wario Land: Shake It, Little King's Story...how can I possibly choose second place? First place is easily Rhythm Heaven Fever, though.
3DS: Luigi's Mansion 2 is my game of the year so far. Kid Icarus comes pretty damn close though, so I'll give it a mention. Also, DKCR 3D could easily beat LM2 but it's a port, and the Wii version is better.
Vita: Uncharted: Golden Abyss. Justified my Vita purchase. Though I haven't beat Rayman Origins on it (played it mostly on 360), but if I could count it then yeah, that. It's the best version of the game imo.
Wii U: New Super Mario Bros U is not only the best 2D Mario game (I haven't played SMB3, yet.), but it's the best 2D platformer of this generation. I regretted my Wii U purchase until I played this game. (Well, and multiplayer Nintendo Land which I want to mention)