A lot of these have been said, but this is my opinion of best series mostly based on how much I liked them and the art style. Ones in bold are my favorite.
Banjo Kazooie
Bomberman
Diddy Kong Racing
Snowboard Kids
Croc
Rayman
Secret of Mana
Mario (Party, Sports, Platformers, Paper)
Pokemon
Advance Wars
Shining Force
Sonic
Animal Crossing
Tales Of Symphonia
Starfox
Yoshi
Legend Of Zelda
Final Fantasy
Gex
Ty the Tasmanian Tiger
Pikmin
Harvest Moon
Mischief Makers
Donkey Kong
Mystical Ninja
Kirby
Bust a Move
Glover
Silicon Valley
Rampage
Chameleon Twist
Metroid
Fire Emblem
Banjo Kazooie
Bomberman
Diddy Kong Racing
Snowboard Kids
Croc
Rayman
Secret of Mana
Mario (Party, Sports, Platformers, Paper)
Pokemon
Advance Wars
Shining Force
Sonic
Animal Crossing
Tales Of Symphonia
Starfox
Yoshi
Legend Of Zelda
Final Fantasy
Gex
Ty the Tasmanian Tiger
Pikmin
Harvest Moon
Mischief Makers
Donkey Kong
Mystical Ninja
Kirby
Bust a Move
Glover
Silicon Valley
Rampage
Chameleon Twist
Metroid
Fire Emblem