They don't need to be in any particular order. It's hard for me to choose...
Playstation 1 (my childhood):
Crash Team Racing
Hot Wheels (something)
Final Fantasy VII
Spider-Man 1 & 2 (ones based off the comics)

Playstation 2:
Shadow of the Colosus
Grand Theft Auto
Kingdom Hearts 1 & 2
Simpsons Skate Boarding & Hit and Run
Ratchet & Clank (all of them)
Need for Speed Most Wanted

Playstation 3:
Infamous 1 & 2
Skyrim & Oblivion
Uncharted Series
Little Big Planet
Killzone 2 & 3
Ratchet & Clank (the good ones )
Resistance Trilogy
Rainbow Six Vegas (couch screen fest with terrorist hunt)
Grand Theft Auto IV and V

Playstation Portable (PSP):
Crisis Core Final Fantasy VII
Ratchet & Clank Size Matters
Sid Meier's Pirates
MidNight Club 3 dub edition
Need for Speed Most Wanted

Now that I think about it, these are just a whole bunch of awesome games that I love!