The Star Wars Battlefront games. With how horribly the liver service EA version that came out in 2015 was and how dead it apparently is, the PS2 games are the only ones I'll ever acknowledge as existing.

Also, one of my personal favorites that I'd consider a must have is Dokopon Kingdom. Yes the remake/remaster exists, but I don't normally go for remasters in most situations. Gameplay is just roll a spinner, move on board, and adventure around the world while trying to do quests if you are in the story mode.

Both games have a lot of content and replayability in my eyes, which makes a game more of a must have for me.

Edit:

Hot Wheels: Beat That! Looked it up because I couldn't remember the name, but that's a racing game with a good amount of replayability and isn't as short as something like Cartoon Network Racing. Didn't realize it came out on various other consoles and PC, but can definitely recommend on at least PS2 (how I ended up playing it).

Gauntlet: Dark Legacy is great classic fun

There are two amazing super hero games that I would recommend: Spider-Man 2 and Hulk: Ultimate destruction.

Spider-Man 2 was easily one of my favorite games of all time. This game essentially set the bar for what a Spider-Man game should be.

Hulk: Ultimate Destruction was an open world game where you were the Hulk and did all the Hulk things. I can't think of a recent game where you play as the green giant.

How is XIII via emulation? Would love to try that on my Steam Deck.

Silent Hill 2

If you're a fan of the anime, the .Hack// games hold up pretty well. There's a little OVA that is included with each game to give more story.

Try out Shin Megami Tensei: Digital Devil Saga 1 and 2. It's one of those JRPG games with a lot of mysteries and loose threads and every single one of them end up solved by the end.

The Soul Reaver / Blood Omen games have not been recommended yet. Though, as a warning, last time I tried to do the Soul Reaver 2, there was a strange bug with the sound that made it so that you couldn't pass a certain puzzle.

I absolutely loved KH1/2 FM

Jak 3

Ace Combat Zero! Or 4, 5, and Zero (in that order) if you want a lot of it.

Dark Cloud 2

Def Jam 2: Fight for NY. It's basically like some of the older WWF wresling games where there can be 4 fighters at a time, but you can only be targetting one at a time. But all the fighters are rappers. The finishing moves are awesome!

Soul reaver

Grand teresmo

Rayman 2

All the GTA games (GTA III, GTA VC, GTA SA, GTA LCS, GTA VCS). There are some good Need for Speed games too, and a bunch of great Tony Hawk games. TimeSplitters, SOCOM, and Red Faction are great too.

...so grain of salt, cuz the name of this one doesn't sound right, but the screenshots look correct: Gradius V?

Side scroller arcade-y jet fighter - I remember it being good.

I just don't remember it being called Gradius >_<

Downhill Domination is... honestly stupid as all hell, but by design: it's a lot of fun :P

It's a downhill mountain bike racing game with a combat system, and it's ridiculous. You start being able to punch the bicyclists next to you; once you knock enough of them off their bikes you upgrade to being able to kick; then iirc you eventually get a stick or something lol. Otherwise, it's just another get-from-point-A-to-B-as-fast-as-possible game that doesn't require a lot of thought.

Arc the lad 2 twilight of spirits is a cult classic

Dance Dance Revolution!

Ratchet and Clank games

My entire childhood was Tony Hawk's Underground 2 on the PS2.

Crash Nitro Kart and some of the PS2 Crash platformers are pretty good. The Kart one has a boosting system that I like better than mario kart (and better items and vibes tbh)

Frequency & Amplitude:

The originators of the modern "rhythm game" genre.

How's PCSX2 performance on the Deck? I somehow get much better performance on my Ryzen 5 4500U laptop than I do on my Ally and that makes absolutely no fucking sense.