PS1:
Final Fantasy VII
Final Fantasy VIII
Final Fantasy IX
Final Fantasy Tactics
Chrono Cross

PS2:
Kingdom Hearts II
Kingdom Hearts: Re:Chain of Memories
Kingdom Hearts
Final Fantasy X
Shadow of the Colossus

PS3:
Nier
The Last of Us
Final Fantasy XIII
Ni no Kuni
Final Fantasy XIII-2

PS4 (so far):
Final Fantasy Type-0 HD
Final Fantasy XIV
Bloodborne
The Order: 1886
Metal Gear Solid V: The Phantom Pain (early copy)

PSP:
Kingdom Hearts: Birth by Sleep
Crisis Core: Final Fantasy VII
Jeanne d'Arc
Dissidia 012 Duodecim: Final Fantasy
Presona 3 Portable

Vita:
Tearaway
Persona 4 Golden
Muramasa Rebirth
Gravity Rush
Uncharted: Golden Abyss

__________________

I hope you do not mind my use of the Persona handheld versions.

PS1:
5) Persona 2: Innocent Sin
4) Final Fantasy VII
3) Xenogears
2) Spyro: Year of the Dragon
1) Final Fantasy IX

PS2:
5) Final Fantasy X
4: Ratchet and Clank: Going Commando
3) Jak 3
2) Dark Cloud 2
1) Persona 4

PS3:
5) Catherine
4) Persona 4 Arena Ultimax
3) Dragon's Crown
2) Valkyria Chronicles
1) The Last of Us

PS1:
- Final Fantasy VII
- Final Fantasy VIII
- Final Fantasy IX
- Dino Crisis 2
- Street Fighter Alpha 3

PS2:
- Final Fantasy X
- Onimusha 3
- God of War
- Metal Gear Solid 3: Subsistence
- Yakuza

PS3:
- Ni No Kuni
-The Last of Us
- God of War 3
- Uncharted 2
- Resident Evil 5 Gold Edition

The only games I remember playing on ps1 are Tekken 3 and Winning eleven 6 and I didn't own a ps3 so here is my top PS2 games:

1. God of war 2
2. Donald Duck: Goin' Qu@ckers
3. Devil May Cry 3
4. Resident Evil 4
5. Scarface: The World Is Yours (I like it more than GTA:SA idec)

PS1:
1. FFVIII
2. Spyro Year of the Dragon
3. Command and Conquer Red Alert Retaliation
4. Digimon World
5. Tvvisted Metal 2

PS2:
1. Final Fantasy X
2. Dynasty Warriors 3
3. Romance of the Three Kingdoms VIII
4. Kingdom Hearrts
5. Disgaea

PS3:
1. Fallout 3
2. Bioshock
3. Uncharted 2
4. Call of Duty Black Ops
5. Disgaea 3

PS1
- Metal Gear Solid
- Gran Turismo 2
- Tekken 3
- Rayman 2: The Great Escape
- CTR

PS2
- Ratchet & Clank 2: Going Commando
- Ratchet & Clank 3: Up Your Arsenal
- God of War II
- Prince of Persia: Warrior Within
- Grand Theft Auto: San Andreas

PS3
- InFamous
- InFamous 2
- Uncharted 3: Drake's Deception
- Metal Gear Solid 4: Guns of the Patriots
- God of War III

PS1
1. MGS
2. RE2
3. Duke nukem time to kill.
4. Triple play 2000.
5. RE1

PS2
1. GTA SA
2. MGS2
3. RE4
4. GOW2
5. DBZ budokai 3

PS3
1. Demon souls
2. TLOU
3. Uncharted 2
4. COD 4 modern warfare
5. Dark Souls

PS1:
1. Metal Gear Solid
2. Digimon World
3. Digimon World 3
4. Resident Evil 3
5. Final Fantasy 7

PS2:
1. Metal Gear Solid 2
2. Metal Gear Solid 3: Subsistence
3. Persona 4
4. Persona 3
5. Yakuza 1

PS3: (Persona 5 and MGS5 are coming - but i buy it on PS4!)
1. Metal Gear Solid 4
2. Yakuza 5
3. The Last of US
4. Ni No Kuni
5. Grand Theft Auto 5

PS1

1) Suikoden II
2) Final Fantasy VII
3) Xenogears
4) Tales of Eternia
5) Grandia

PS2

1) Persona 4
2) Yakuza 2
3) Final Fantasy X
4) Suikoden III
5) Xenosaga: Der Wille zur Macht

PS3

1) The Last of Us
2) Uncharted 2: Among Thieves
3) Metal Gear Solid 4: Guns of the Patriots
4) Ni no Kuni
5) Tales of Xillia

PS1-
1. Red Alert Retaliation
2. Devils Deception
3. FFVII
4. Theme Hospital
5. Spyro 3

PS2-
1. FFX-2
2. FFX
3. Motor Seige
4. Starwars battlefront 2
5. FF12

PS3-
1. Just Cause 2
2. Civilization Revolution
3. Journey
4. Fallout 3
5. Oblivion