Metal Gear Solid 2 and 3 (and go back and play 1 first, if you haven't).

Only other thing that comes to mind is FFX. Just try to resist min/maxing too much. Very unsatisfying to spend tons of hours grinding your characters into unstoppable gods and then go one-shot the final boss.

I had a ton of fun with Unreal Tournament. I got into the zone while playing Instagib CTF.

We played the hell out of Shaun Palmer’s snowboarding. And I’m pretty sure we hammered Tony Hawk too.

Gun

Tmnt

Wild ARMS 3 Godzilla: Save the Earth

I see you've got 007: Nightfire in that list, so let me raise you 007: Agent Under Fire. The single player is not as good as Nightfire, but the multiplayer is spectacular, as it lets you turn on fun modifiers like moon gravity and use gadgets like the Q Claw on any surface instead of just preset spots. They probably toned down the multiplayer in Nightfire because Agent Under Fire's didn't feel very Bond-esque, but Bond or not, it was a ton of fun. The multiplayer is up to 4 players split-screen on Gamecube, but I can't tell if it still retains that on PS2; often times, back then, PS2 games only had 2 player support while Gamecube and Xbox had 4. This was because the PS2 was weaker and also required an extra peripheral called a Multi Tap to hook up more than 2 controllers. Find some friends and play some deathmatch, if you find yourself in a situation where you can dock your Steam Deck or otherwise play on another computer.

There's also Metal Arms: Glitch in the System, a third person shooter where you play a robot who can take over other robots. It's quite challenging, it's got a sense of humor, and it's probably one of the best games of that era to not get remastered in a modern port. Once again, we've got the multiplayer issue rearing its head, but I'd strongly recommend the single player for this one, too. I also played this on Gamecube back in the day, so just play whichever version is rated best for compatibility in your emulator of choice.

You might also want a Burnout game in your library. Most people seem to prefer Burnout 3: Takedown, but my Burnout of choice was Burnout Revenge. Both great. I wish we got more racing games like these today. Local multiplayer is a dying breed in this genre.

You've got Tony Hawk's Underground in that list, but for my money, the best game in the series is Tony Hawk's Pro Skater 3.

The first three Ratchet & Clank games on PS2 have not been topped by their later entries, as far as I'm concerned. Ever since the fourth game, Deadlocked, the best they've been able to do was to remix ideas they've already used.

Tony Hawk's Pro Skater 3 was pretty close to the peak of the series if you ask me, and the PS2 version was the superior one. THPS4 also came out on the Playstation 2. I see you already have Underground on there.

If you'd like something you can handily use to consume the rest of your entire life, Disgaea and/or its sequel will probably do you.

Ico and Shadow of the Colossus are also legendary. I haven't tried in ages, I have no idea if modern emulators can get the latter to run at a non-crap frame rate. It'd be a lot nicer if so.

Odin Sphere is an often overlooked 2D action sidescrolling fighting thing wherein you Norse In The North and beat the shit out of absolutely everyone. Its sequel, Muramasa: The Demon Blade is much the same thing except therein you Ninja In The Night instead. The latter stayed locked to the Wii to my knowledge but the former was on the PS2.

The PS2's library is quite vast. I'm not going to go looking this up to prove it right now, but I'm pretty sure it's got the most titles ever released for a home video game console (i.e. not the PC) in history. Even just trying out unknown games at complete random, it's likely to be able to keep you entertained in one way or another basically forever.

Midnight Club 2

Not sure how well it holds up since nobody mentions it, but Tiny Tank was fun when I was a kid!

You're a sarcastic tank and fight other huge robots after they took over the world basically. You have 4 spots on your tank to put a lot of different weapons and could upgrade them during the level with positronic brains from enemies to make them more advanced (e.g. homing missiles, faster firing, etc.)

So judging from the comments, there is your ps2 games recommendations: the entire PlayStation 2 library.

• Silent Hill 2, obviously.

• Kuon - FromSoftware

• Ghost in the Shell Stand Alone Complex

• Robotech Battlecry (the Xbox release was better, but the PS2 one is fine)

• Berserk Millennium Falcon Arc (there is an English patch)

• Shadow Tower Abyss (there is an English patch)

• Castlevania: Lament of Innocence & Curse of Darkness

• Haunting Ground

• Ultimate Spiderman

• Winback

• Xenosaga 1-3

• Cold Fear (PC version is probably a better pick though)

Lots of good suggestions from everyone.

No one mentioned Mr Moskeeto though!

If you've never played the genre before, I'd throw dynasty warriors at you. Pick whichever was the highest number available, because quality of life improved so much for each one. It's an endless sea of mooks that you smash through until you come up against the wall that is... LU BU!!!

https://en.wikipedia.org/wiki/List_of_best-selling_PlayStation_2_video_games

I'd just start reading at the top and play some that look fun. Sales are a fair proxy for "good" games. I'm sure there are ratings lists too, if you feel so inclined.

(You can probably skip all the sports games, though.)

NBA Street Vol 2 or V3. Never found another sports game that's as much fun.

Games only last a few minutes and there's no concept of seasons or anything. It's just casual streetball where no rules matter - including the rules of physics.

Silent Hill 2 and Fatal Frame

Gitaroo Man!

I only played it recently but it really feels like an underrated gem that you don’t see mentioned that often in lists of “best PS2 games”

It’s a rhythm game with goofy visuals and cutscenes. Also super hard at points but the music is great!

Dragon Ball Z Budokai Tenkaichi 2 or 3

Primal is a game that got a lot of hype at the time but nobody ever seems to talk about any more. No remaster, no sequel, nothing.

May have been suggested already but Arc the Lad: Twilight of the spirits

It's an interesting story who's main overarching theme is messy families. The protagonists family gets separated very early at their birth, fathers lose their families and vice versa.

I recommend giving graffiti kingdom a try. It's a 3d platform er where you draw your own character.

Haunting Ground