I'd had some game consoles before, some no-name brands that played pong and of course, I had the PC. The Playstation 2 was my first real console. We bought it for the kids who were very little at the time and we bought it in the last years of its life, which meant that there were literally hundreds of playable second hand titles about. It felt obvious that we'd upgrade to the PS3 and stick with Sony all the way ... and then Sony decided to lose compatibility.. and that was the end of Sony for our family.
We replaced it with an XBox and the kids grew up and I couldn't get near the consoles so I went back to PC.
God of War I and II
I always loved Greek Mythology and the God of War games were simply incredible.
Lego Star Wars 1 & 2
The ones that started it all. Lego games have since become a genre to themselves.
Star Wars: Revenge of the Sith
Arguably one of the best Star Wars games ever, and so far, not remade for the PC. This one was incredible.
Soulcalibur III
Getting bashed up by sexy girls. What's not to like. Even when you lose, you win.
There weren't a lot of games on PS2 that I managed to get all the way through to "total completion" but there were a few (and at the time, there were more on this platform than on any other).
Crash Tag Team Racing
Dogz
God of War 1
God of War 2
Half-Life 1
Harry Potter and the Order of the Phoenix
Lego Indiana Jones 1
Lego Star Wars 1
Lego Star Wars 2: The Original Trilogy
The Polar Express
Star Wars: Revenge of the Sith
Scooby Doo: Mystery Mayhem
Soul Calibur III
Stuart Little
The games in this category are still games I'd recommend because I got a lot out of them. It's just the OCD part of me that has a problem with not being able to finish them.
The Hulk
This was an open-world hulk game. It was really great and I got most of the way through it but just never finished some of the levels
The Simpsons Hit & Run
This was one of the first games we got for PS2 and it was probably the most played in our family (apart from Star Wars Battlefront I and II which I didn't get near).
Animaniacs: The Great Edgar Hunt
Awesome and completed right up to I think the very last scene (the Zeppelin) which was just too hard and spoilt it for me.
Jak and Daxter: The Precursor Legacy
Another one that I finished all the way up to the last scene where they just made it too difficult to complete.
The games in this category were good too but for one reason or another, I stopped playing them. Usually because I got distracted by something else.
Bee Movie
Ben 10
Cars
Crash Nitro Kart
Crash of the Titans
Crash: Mind Over Mutant
DOA
Echo Night: Beyond
Eragon (This game was much better than the movie or the book)
Evil Dead: A Fistful of Boomstick
Franklin: A Birthday Surprise (Easy but not exactly engaging)
Harry Potter and the Chamber of Secrets (was starting to get difficult)
Harry Potter and the Prisoner of Azkaban
Jak 3 (decided to do Jak II first but couldn't get started on it).
King Kong
Looney Tunes: Acme Arsenal
Over the Hedge
Ratchet & Clank: Locked & Loaded
SSX 3
Star Wars: The Clone Wars
Star Wars: Battlefront
Star Wars: Battlefront II
Wallace & Gromit: The Curse of the Were-Rabbit
When the PS2 was ending, everthing became very cheap and I picked up a lot of games at bargain prices but then never found the time to play them. Maybe when I'm in an old person's home...
Aliens Versus Predator: Extinction
Bionicle: The Game
Black
Brothers In Arms: Road to Hill 30
Escape from Monkey Island
Fantastic Four
Ghostbusters: The Video Game
Grand Theft Auto: San Andreas
Harry Potter and the Goblet of Fire
Harry Potter and the Half-Blood Prince
Hunter: The Reckoning: Wayward
Indiana Jones and the Staff of Kings
The Legend of Spyro: Dawn of the Dragon
Lego Batman
The Matrix: Path of Neo
Pirates of the Caribbean: The Legend of Jack Sparrow
Predator: Concrete Jungle
Prince of Persia: The Sands of Time
Prince of Persia: The Two Thrones
Prince of Persia: Warrior Within
Quake III Revolution
Ratchet & Clank: Size Matters
Rayman Raving Rabbids
Red Faction 1 (also got this for the PC and will probably play it there)
Red Faction 2 (also got this for the PC and will probably play it there)
Return to Castle Wolfenstein: Operation Resurrection (Played it on PC instead)
Rumble Roses
Tomb Raider: The Angel of Darkness
The games in this category are generally games I wouldn't recommend that any beginners to play. They're too frustrating.
Burnout (I don't think anyone in our house has ever completed a race)
Crash Bandicoot: The Wrath of Cortex
GoldenEye: Rogue Agent
The Simpsons Game - Got stuck on about the second level (Planetarium) and lost interest.
Harry Potter and the Philosopher's Stone
Jak II
Kingdom Hearts (Started off hard and got harder - and seemed to be going nowhere)
The Lord of the Rings: The Return of the King
Ratchet & Clank: Up Your Arsenal
Rayman 2: Revolution
Resident Evil Code: Veronica X (I die in my first zombie scene every time).
Star Wars: Bounty Hunter
Star Wars: Starfighter - Never actually made it to a battle
Terminator 3: The Redemption
Wacky Races Starring Dastardly and Muttley