Playstation 1:
1. Crash Team Racing
2. Hogs of War
3. Crash Bandicoot 3
3. Tekken 3
5. Rayman Rush

Playstation 2:
1. Grand Theft Auto San Andreas
2. Tekken 5
3. Ratchet & Clank 3
4. Smackdown vs Raw 2008
5. Crash Bandicoot: Wrath of Cortex

Playstation 3:
1. Grand Theft Auto V
2. Dark Souls
3. Tekken Tag Tournament 2
4. Uncharted 2: Among Thieves 
5. Dark Souls 2

PS1
1. Castlevania: Symphony of the Night
2. Resident Evil 2
3. Metal Gear Solid
4. Final Fantasy VII
5. Xenogears

PS2
1. Virtua Fighter 4: Evolution
2. God of War II
3. Metal Gear Solid 3: Snake Eater
4. Grand Theft Auto: San Andreas
5. Okami

PS3
1. The Last of Us
2. Uncharted 2: Among Thieves
3. Batman: Arkham City
4. Call of Duty 4: Modern Warfare
5. Grand Theft Auto V

PSP
1. Metal Gear Solid: Peace Walker
2. God of War: Chains of Olympus
3. Shin Megami Tensei: Persona 3 Portable
4. Syphon Filter: Dark Mirror
5. Grand Theft Auto: Liberty City Stories

PS1:
Final Fantasy VII
Street Fighter Ex Plus
Street Fighter Alpha 3
Bust a groove
Tekken 3

PS3:
Final Fantasy XIII-2
South Park
Ni No Kuni
Uncharted 2 and 3 (haven't finished yet)

PS1:
Final Fantasy VII
Metal Gear Solid
Final Fantasy Tactics
Fear Effect 2
Soul Blade
(Narrowing it down was hard!)

PS2
Metal Gear Solid 3
Tomb Raider Legend
Final Fantasy X
Grand Theft Auto San Andreas
SSX3

PS3
Valkyria Chronicles
Uncharted 2
God of War 3
Little Big Planet 2
Heavy Rain

(I have a PSP and Vita, too....)

In no particular order...

PS1
Final Fantasy Tactics
Final Fantasy 9
Vagrant Story
Xenogears
Mortal Kombat Trilogy

PS2
Final Fantasy XII
Final Fantasy X
Dragon Quest VIII
Mortal Kombat: Deception


PS3
Mass Effect Trilogy
Bioshock
Catherine
Bioshock Infinite
Dead Space