I've been getting back into playing the PS2 library via emulation, although I do have a real PS2 and a biiiiig stack of discs (many legit even).
There are definitely a lot of games I'm missing out on.

Some of what I've been playing or have played are:
(o) Silent Scope 1 and 2 (they support USB mice natively! shit feels great)
(o) the Tekken games (especially the side modes - Devil Within is super jank in Tekken 5, and I wish my cheapo USB Xinput controller had a better analog stick since it is nowhere near precise enough to do Starblade with)
(o) the Taiko no Tatsujin games (I wish I could plug random USB controllers into the PS2 and they'd work - emulation isn't unplayable, but the latency is... well, it is more than I'd like)
(o) Ape Escape 2 and 3 (I like 3 more than 2; Yumi/Sayaka is ez mode since she gets a bunch of free monkeys that don't run from her, but she's cuter, so I play as her every single time)
(o) Twinkle Star Sprites (the sequel, very cute, very fun, I don't like Load Run's new outfit here but she's not the main character of this game)
(o) Dead or Alive 2 (yes, it's an RPS game, but fuck man, that's fighting games, DOA just makes it really fucking explicit)
(o) Burnout 2 and 3 (god, these games are so fucking good)
(o) the Ace Combats (I've spent the most time with AC4 out of the PS2 games; the AC game I've spent the longest with period was actually AC2 on PS1)

there are definitely a few things I've spent nowhere near as much time as I should have with (in particular, I've played a lot of the PS1 Armored Core games, but basically nothing of the PS2 series)
and surprisingly enough, I've never played any of the God of War games

What does Heyuri like on the PS2?
or fuck, PS1 too