If 2D Mario platformers count as their own contiguous series, Super Mario World -> New Super Mario Bros.
Yoshi's Island -> Yoshi's Story
Final Fantasy Tactics -> Final Fantasy Tactics Advance
Wario Land 4 -> Wario: Master of Disguise
Golden Sun II -> Golden Sun: Dark Dawn
Crazy Taxi -> Crazy Taxi 2
Mirror's Edge -> Mirror's Edge: Catalyst
Contra: Hard Corps -> Contra: Legacy of War
Castlevania -> Castlevania II: Simon's Quest
Castlevania: Symphony of the Night -> Castlevania 64
Suikoden V -> Suikoden Tierkreis
Gradius V -> Otomedius
KONAMIIIIIIIIIIIII
In terms of spritual sequels, Panzer Dragoon Orta -> Crimson Dragon
Yoshi's Island -> Yoshi's Story
Final Fantasy Tactics -> Final Fantasy Tactics Advance
Wario Land 4 -> Wario: Master of Disguise
Golden Sun II -> Golden Sun: Dark Dawn
Crazy Taxi -> Crazy Taxi 2
Mirror's Edge -> Mirror's Edge: Catalyst
Contra: Hard Corps -> Contra: Legacy of War
Castlevania -> Castlevania II: Simon's Quest
Castlevania: Symphony of the Night -> Castlevania 64
Suikoden V -> Suikoden Tierkreis
Gradius V -> Otomedius
KONAMIIIIIIIIIIIII
In terms of spritual sequels, Panzer Dragoon Orta -> Crimson Dragon