Not exactly the best games in a franchise, but just which game enterprises whose soul, characters and stories and memories you most fondly enjoy.
Common candidates are:
-Mario
-Sonic
-Metroid
-Castlevania
-Contra
-MegaMan
-King of Fighters
-Samurai Shodown
-Fatal Fury
-Metal Slug
-Last Blade
-Ninja Gaiden
-Shinobi
-Strider
-ThunderForce
-Gradius
-Mario Kart
-Street Fighter
-Mortal Kombat
-NBA Jam
-Doom
-Madden
-Tetris
-Puyo Puyo
-Silent Hill
-Resident Evil
-Streets of Rage
-Final Fight