Phoenix Wright/ Apollo Justice (best story ever on DS for me, not an RPG though)
Prof. Layton DB/CV (2nd best story ever on DS for me)
KH (3rd best story for me)
And then, in no particular order....
Chrono Trigger
FF III and IV (although if you have a PS1/2/P or GB FF VI and VII has better story)
TWEWY
Time Hollow
Hotel Dusk
DQ IV/V/IV
SMT
S and SMT: SJ
Trace Memory
Knights in Nightmare
Suidoken
Disgea
Soma Bringer
Fire Emblem
Final Fantasy CC: RoF/EoT (RoF was better in terms of story, EoT in gameplay)
Pokemon: Mystery Dungeon (these have much better story than Pt/P/D)
GTA: CW
COP
Luminous Arc
Avalon Code
M&L 2/3
Castlevania (all of them)
Sonic: Dark Brotherhood
Sands of Destruction
Henry Hastworth
FFXII: RW
Metroid
Trauma Center 1/2
Yoshi's Island
Super Robot Taisen
Nostalgia
Pokemon Ranger 2 (the first one's story was boring)
Zelda (good to some people, for me, meh)
Tales of Hearts
Tales of Innocence
SaGa 2
Valkyrie Profile: Covenant of the Plume
Rune Factory 1/2
Nanashi no Geemu (if it ever gets translated)
All I can think of. Hope it helps.