I have played a ton of respectable, non violent games that are on Sony systems. You can find almost if not all of them on the PS3 marketplace.
I really recommend Sony for kid games over Microsoft, and of course Nintendo overall since they make the best family friendly games, and everybody in general, but these games are all awesome, and they come very close to Nintendo in what you'd be looking for.
This took a good half hour to put together, I was very diligent towards the cause.
PS1:
Crash Bandicoot
Crash Bandicoot 2
Crash Bandicoot 3: Warped
Crash Team Racing
PaRappa the Rapper
Spyro The Dragon
Spyro 2: Ripto's Rage
Spyro 3: Year of the Dragon
WipeOut
WipeOut 2097
Wipeout 3 (kinda like F-Zero with powerups/combat)
Rayman
Rayman 2
Rayman 3
Ape Escape
PS2:
Ico
Ape Escape 2
Ape Escape 3
PaRappa the Rapper 2
Katamari Damacy
We <3 Katamari
Kingdom Hearts
Kingdom Hearts 2
Jak and Daxter
Jak 2
Jak 3
Jak X Racing
Sly Cooper and the Thievius Raccoonus
Sly 2: Band of Theives
Sly 3: Honor Among Theives
Wipeout Pulse
Ratchet and Clank
Ratchet and Clank: Going Commando
Ratchet and Clank: Up Your Arsenal (despite racy names, really kid friendly)
PS3:
Little Big Planet
Little Big Planet 2
Little Big Planet: Karting
Sly Cooper: Theives in Time
Katamari Forever
3D Dot Game Heroes
Ratchet and Clank Future: Tools of Destruction
Ratchet and Clank Future: Quest for Booty
Ratchet and Clank Future: A Crack in Time
Ratchet and Clank: All 4 One
Ratchet and Clank: Into the Nexus
WipeOut HD
ModNation Racers
Spelunky
Joe Danger
Joe Danger 2: The Movie
Journey
Mini Ninjas
Sound Shapes
Tokyo Jungle (A bit of violence, but overall funny and lighthearted)
Super Stardust HD
Puppeteer
Ni No Kuni: Wrath of the White Witch (made by classic animated movie producer Studio Ghibli)
PS4:
Octodad: Dadliest Catch
Knack
Resogun
Don't Starve
Pinball Arcade
Towerfall: Ascension
PSP:
Ape Academy
Ape Academy 2
Ape Escape P
Mercury
Bomberman Land
Lemmings
Bubble Bobble Evolution
Lumines
Every Extend Extra
Invizimals
Kingdom Hearts: Birth By Sleep
Little Big Planet
LocoRoco
LocoRoco 2
Patapon
Patapon 2
Patapon 3
Me and My Katamari
Rock Band Unplugged (lyrics can sometimes be off colored, but it's just music)
Sonic Rivals
Sonic Rivals 2
Daxter
Secret Agent Clank
WipeOut Pure
PixelJunk Monsters
Hatsune Miku: Project Diva
Vita:
WipeOut 2048
Little Big Planet
Super Stardust Delta
Smart As...
Touch My Katamari
Tearaway
Lumines: Electronic Symphony
ModNation Racers: Road Trip
Little Deviants
PixelJunk Monsters: Ultimate
OlliOlli
Dokuro
Hatsune Miku: Project Diva f 2nd
Sorcery Saga: Curse of the Great Curry God
There's also a lot of games still to come on the PS4 and Vita since they're relatively new, so the list is expected to grow.
And of course sports games (even though you said not to, these are PS only games that are very fun despite being sports related:
Hot Shots Golf (PS2, PS3, PSP, Vita) (very fun mini golf game)
MLB: The Show 08-14 (PS2, PS3, PS4, PSP, Vita)
Gran Turismo 1-6 (PS1-PS3)
Motorstorm
Motorstorm: Arctic Edge
Motorstorm: Pacific Rift
Motorstorm: Apocalypse
Also, on both PS3 and Vita:
Playstation All Stars: Battle Royale (pretty much Smash Bros with Sony characters)
Rayman Origins
Rayman Legends
Bit Trip Runner 2
Spelunky
Fl0w
Flower
Terraria
Minecraft
Hatsune Miku: Project Diva f
That isn't even touching a good deal of the kid friendly games that aren't only on Sony systems. You still have your Sonics, LEGOs, and countless others.
I have played a ton of respectable, non violent games that are on Sony systems. You can find almost if not all of them on the PS3 marketplace.
I really recommend Sony for kid games over Microsoft, and of course Nintendo overall since they make the best family friendly games, and everybody in general, but these games are all awesome, and they come very close to Nintendo in what you'd be looking for.
This took a good half hour to put together, I was very diligent towards the cause.
PS1:
Crash Bandicoot
Crash Bandicoot 2
Crash Bandicoot 3: Warped
Crash Team Racing
PaRappa the Rapper
Spyro The Dragon
Spyro 2: Ripto's Rage
Spyro 3: Year of the Dragon
WipeOut
WipeOut 2097
Wipeout 3 (kinda like F-Zero with powerups/combat)
Rayman
Rayman 2
Rayman 3
Ape Escape
PS2:
Ico
Ape Escape 2
Ape Escape 3
PaRappa the Rapper 2
Katamari Damacy
We <3 Katamari
Kingdom Hearts
Kingdom Hearts 2
Jak and Daxter
Jak 2
Jak 3
Jak X Racing
Sly Cooper and the Thievius Raccoonus
Sly 2: Band of Theives
Sly 3: Honor Among Theives
Wipeout Pulse
Ratchet and Clank
Ratchet and Clank: Going Commando
Ratchet and Clank: Up Your Arsenal (despite racy names, really kid friendly)
PS3:
Little Big Planet
Little Big Planet 2
Little Big Planet: Karting
Sly Cooper: Theives in Time
Katamari Forever
3D Dot Game Heroes
Ratchet and Clank Future: Tools of Destruction
Ratchet and Clank Future: Quest for Booty
Ratchet and Clank Future: A Crack in Time
Ratchet and Clank: All 4 One
Ratchet and Clank: Into the Nexus
WipeOut HD
ModNation Racers
Spelunky
Joe Danger
Joe Danger 2: The Movie
Journey
Mini Ninjas
Sound Shapes
Tokyo Jungle (A bit of violence, but overall funny and lighthearted)
Super Stardust HD
Puppeteer
Ni No Kuni: Wrath of the White Witch (made by classic animated movie producer Studio Ghibli)
PS4:
Octodad: Dadliest Catch
Knack
Resogun
Don't Starve
Pinball Arcade
Towerfall: Ascension
PSP:
Ape Academy
Ape Academy 2
Ape Escape P
Mercury
Bomberman Land
Lemmings
Bubble Bobble Evolution
Lumines
Every Extend Extra
Invizimals
Kingdom Hearts: Birth By Sleep
Little Big Planet
LocoRoco
LocoRoco 2
Patapon
Patapon 2
Patapon 3
Me and My Katamari
Rock Band Unplugged (lyrics can sometimes be off colored, but it's just music)
Sonic Rivals
Sonic Rivals 2
Daxter
Secret Agent Clank
WipeOut Pure
PixelJunk Monsters
Hatsune Miku: Project Diva
Vita:
WipeOut 2048
Little Big Planet
Super Stardust Delta
Smart As...
Touch My Katamari
Tearaway
Lumines: Electronic Symphony
ModNation Racers: Road Trip
Little Deviants
PixelJunk Monsters: Ultimate
OlliOlli
Dokuro
Hatsune Miku: Project Diva f 2nd
Sorcery Saga: Curse of the Great Curry God
There's also a lot of games still to come on the PS4 and Vita since they're relatively new, so the list is expected to grow.
And of course sports games (even though you said not to, these are PS only games that are very fun despite being sports related:
Hot Shots Golf (PS2, PS3, PSP, Vita) (very fun mini golf game)
MLB: The Show 08-14 (PS2, PS3, PS4, PSP, Vita)
Gran Turismo 1-6 (PS1-PS3)
Motorstorm
Motorstorm: Arctic Edge
Motorstorm: Pacific Rift
Motorstorm: Apocalypse
Also, on both PS3 and Vita:
Playstation All Stars: Battle Royale (pretty much Smash Bros with Sony characters)
Rayman Origins
Rayman Legends
Bit Trip Runner 2
Spelunky
Fl0w
Flower
Terraria
Minecraft
Hatsune Miku: Project Diva f
That isn't even touching a good deal of the kid friendly games that aren't only on Sony systems. You still have your Sonics, LEGOs, and countless others.