Here's a list I've compiled (and will add to) of games you should probably own for each system I own.
DS:
Pokemon (Doesn't matter which)
New Super Mario Bros.
Rhythm Heaven
Mario Party DS
Golden Sun: Dark Dawn
Luminous Arc
Lunar Knights (FANTASTIC game made my the people who brought you MGS)
Burnout Legends
Disgaea
PSP:
MGS: Peace Walker
Person 3 Portable
Prinny: Can I Really Be The Hero?
Disgaea 1, 2, and Infinite
Dissidia: Final Fantasy
Final Fantasy I
Me and My Katamari
Phantasy Star Portable 2
Metal Slug
LittleBigPlanet
R&C: Size Matters
Fat PrincesS: Fistful of Cake
Riviera: The Promised Land
Patapon 1/2
Wii:
NSMBWii
Monster Hunter Tri
SSBB
Rock Band 2/3
PS3:
Uncharted 1/2
Disgaea 3
Final Fantasy XIII
God of War 1/2/3
Borderlands
Fat Princess
Flower
Dragon Age
Lost Planet 2
Trinity Universe
BlazBlue: Continuum Shift
Elder Scrolls IV: OBLIVION
NFS: Hot Pursuit
RDR
Demon's Souls
LittleBigPlanet (wait for 2)
Sims 3
Butnout Paradise
Katamari Forever
3D Dot Game Heroes
Ratchet and Clank: Crack in Time
ModNation RAcers
inFAMOUS
DS:
Pokemon (Doesn't matter which)
New Super Mario Bros.
Rhythm Heaven
Mario Party DS
Golden Sun: Dark Dawn
Luminous Arc
Lunar Knights (FANTASTIC game made my the people who brought you MGS)
Burnout Legends
Disgaea
PSP:
MGS: Peace Walker
Person 3 Portable
Prinny: Can I Really Be The Hero?
Disgaea 1, 2, and Infinite
Dissidia: Final Fantasy
Final Fantasy I
Me and My Katamari
Phantasy Star Portable 2
Metal Slug
LittleBigPlanet
R&C: Size Matters
Fat PrincesS: Fistful of Cake
Riviera: The Promised Land
Patapon 1/2
Wii:
NSMBWii
Monster Hunter Tri
SSBB
Rock Band 2/3
PS3:
Uncharted 1/2
Disgaea 3
Final Fantasy XIII
God of War 1/2/3
Borderlands
Fat Princess
Flower
Dragon Age
Lost Planet 2
Trinity Universe
BlazBlue: Continuum Shift
Elder Scrolls IV: OBLIVION
NFS: Hot Pursuit
RDR
Demon's Souls
LittleBigPlanet (wait for 2)
Sims 3
Butnout Paradise
Katamari Forever
3D Dot Game Heroes
Ratchet and Clank: Crack in Time
ModNation RAcers
inFAMOUS