Every single portable, and console, in gaming history, should have at least one game that everyone likes. If not, you might be a little too narrow minded. That's what I think.
Anyways, to be honest with you, I have always liked the Nintendo 64 games, and Gamecube games, more than Playstation, Playstation 2, and Xbox games. Then again, I only have a handful of games for each console. On my Gamecube, I have Wind Waker, Smash Bros. Melee, Super Mario Sunshine, and Mario Kart: Double Dash!!, which are amongst my favorite games. I couldn't care less for anything else on the Gamecube. I grew up with Nintendo, so that's why I like their games better. I got into video games in the Nintendo 64, Sega Saturn, and Playstation era, which explains why I like Mario, Sonic, and Crash so much; Well, I didn't like Sonic when he hit the Sega Saturn (damn Sega for cancelling Sonic Xtreme. I swear, that project-S better bring it back soon).
When the geneartion before this generation arrived, I only bought games that brought nostalgia, but since Donkey Kong, Crash, and Sonic, sucked, all I was left with was Zelda, and Mario, which really pissed me off. I liked the first Jak game, and Ratchet and Clank games. They kind of filled the emptyness a little. Halo was also cool. It brought me into the world of first person shooters. I just felt the generation lacking a little bit.
At the end, there is at least one game, in every single console, and portable, that I liked, or want to play.
Long live the Wii!