Some video game narratives are good enough to spawn several sequel and prequel games. For better or for worst. Here are my personal favorite 6 video game series as of right now.
#6 - The Paper Mario series: Paper Mario, Paper Mario the Thousand Year Door, Super Paper Mario and Paper Mario Sticker Star.
#5 - Shin Megami Tensei Persona : Persona, Persona 2: Eternal Punishment, Persona 3: FES, Persona 4 Golden, Persona Q, Persona 4 Arena Ultimax. Also...Persona 4 Dancing All Night...
#4 - Ace Attorney Series: Ace Attorney: Phoenix Wright, Ace Attorney: Justice For All, Ace Attorney: Trials and Tribulations, Apollo Justice: Ace Attorney and Ace Attorney: Dual Destinies. There's also the Miles Edgeworth spin-offs.
#3 - Zero Escape: Nine Hours, Nine Persons, Nine Doors and Virtue's Last Reward.
#2 - Danganronpa: Danganronpa: Trigger Happy Havoc, Danganronpa: Ultra Despair Girls and Danganronpa 2: Goodbye Despair.
#1 - Kingdom Hearts: KH1, KH CoM, KH2, KH 358/2 Days, KH Birth By Sleep, KH: Coded and Kingdom Heart 3D: Dream Drop Distance.
Honorable mentions: Legend of Zelda, Fire Emblem, Professor Layton and Disgaea.