I missed quite a bit back then, but for what I did manage to play, my top 5 were incredible experiences. In no particular order:
Half-Life PS2 - I didn't need a PC to know that I was playing one of the best first person shooter campaigns of all time, and after playing the PC version, this PS2 version felt more like the definitive edition. Not only that, but Half-Life PS2 came out at the exact same time as Halo 1 and managed to figure out first person shooter controls on console
at the exact same time, which not many people bother to bring up historically.
Plus it led to a fun interaction with a friend:
Me: "Man, Half-Life was unforgettable. It had great theme music too."
Friend: "Half-Life had theme music?"
Me: "It always did. Listen to this."
Final Fantasy X - There is no other JRPG with such a setting as Spira. An oceanic world based on water/spirits, water gods, underwater sports, etc. It felt thematically consistent throughout to the point where it felt like an actual world I could go to compared to most other games. It was unique at the time and still remains unique to this day.
Lastly it just looked gorgeous on the PS2 and has a
soundtrack that I would consider to be equivalent to a Skyrim of it's generation:
Grand Theft Auto 3 - I know that people hold Vice City and San Andreas in higher regard, but for me this game managed to stand out above both. Unlike the sequels, it kept things simplistic since you were mainly a Mr. fix-it/hitman-esque character the entire game. You're given an objective or target, you are told to take care of said target by any means 99% of the time, and you get paid upon completion.
The map itself wasn't too large or bloated and every other system in the game felt like a bonus rather than a requirement or secret requirement. Something was lost when rockstar kept making their sequels and the games became more, and more, and more constricted over time. Another game with a great theme song:
Godhand - This would be the equivalent of that random Steam game you'd find today that looked a bit janky but fun from footage, and you end up having a blast the entire time. A 3rd person shooter-cam zany japanese beat em up that still doesn't quite have it's own 1:1 successor in what it manages to accomplish. I consider it PS2 generation's Metal Gear Revengeance.
SSX 3 - My own personal pinnacle of sports games representing EA at their peak in performance. Even playing it recently on Xbox Series X Backwards Compat, it still controlled beautifully and was a blast to play. It also introduced me to a ton of great bands, as EA has been well known for doing. It's worth checking out to this very day.
The only game on my list that has aged poorly
in terms of controls is GTA 3. The rest, I'd easily recommend at any time.