Hmmm my favorite genres from most fave to least fave are RPG's, Platformer, New Ideas,Adventure,3d fighters,2d fighters, racers,Arcade sports,3rd person shooters, FPS, Puzzle, and Finally Sim sports.
My favorite games are The Legend of Zelda:LTTP,Links Awaking,Windwaker. The only Zelda games I have not beat is the first 2 on the Nes,Majora's Mask, and the Oracle games.
Do you have the Zelda Collection? That would be a good place to start with the Zelda games.
The Mario games I like are Galaxy, world,3 are my favorites in that series. With Metroid my only experience with them was Super Metroid,and the Prime Trilogy.
My favorite Rpgs are Tales of Symphonia and Skies of Arcadia Legends, SMRPG, I like the Paper Mario Series. Out of those I like The Thousand Year Door, The Mario and Luigi series: my favorite is Super Star Saga and there is going to be a third in the series on the DS.
The Fighters I like are Weapon based fighters like Soul Calibur 2 and Samuri Shodown, SF2 and the Smash Brothers series.
Racers I like fun racers like Mario Kart and Futurestic ones like F-Zero.
I wasn't a fan of shooters in the past but the Wiimote changed my opinion of them.
Most of my favorite games are first party but out of third party I like RE4, Megaman 9,3,2,4, castlevania 3 and Aria of Sorrow, Ninja Gaiden on the NES. Sonic 2 and 3.Secret of Mana.