In no particular order…

• Sly Cooper trilogy. The second game is the best, but the third has its strong points too. The first game feels like a tech demo in comparison to the second.
• Final Fantasy X (though I’d actually recommend playing it on PC with the Untitled Project X mod)
• Ratchet and Clank. The second and third games are the best. Deadlocked is divisive for many fans.
• Jak and Daxter trilogy. 2 and 3 are very different from the first game.
• GTA San Andreas.
• Kingdom Hearts 1 & 2. Ideally you should actually play these on the PS4/PS5/PC, because those are the directors cut (Final Mix) versions of the games. You can’t skip Chain of Memories either, which was originally only available on the GameBoy Advance; Look up a plot summary if you don’t want to play CoM, because the gameplay is very different from KH1 and 2.
• Shin Megami Tensei: Nocturne, Persona 3FES, and Persona 4. Nocturne is from the mainline SMT series, while the Persona games are a spin-off. All three are available on other systems as well, (P3FES recently got a remake, for instance).
• Devil May Cry 3: Dante’s Awakening. It’s a prequel, so you don’t need to play DMC 1 or 2 first.
• Metal Gear Solid 3: Snake Eater. It’s also a prequel, so you don’t need to play MGS 1 or 2 first. MGS Subsistence is the director’s cut version of the game, with some added gameplay improvements.
• Okami. If you like Zelda games, you’ll enjoy this. The combat is more akin to a DMC/God of War hack-n-slash, but the dungeons feel like Zelda dungeons.
• Resident Evil 4. The recent remake is also stellar.
• Shadow of the Colossus. Don’t read anything about it beforehand. Go in blind.
• Odin Sphere. A hand-drawn side scroller, with a great story.
• Viewtiful Joe. Same devs as Okami, also cell shaded but with a very different art style. Stylish, fast paced side scroller.
• Psychonauts. 3D platformer with a wild setting.
• God of War trilogy. See where the series started, because the recent games are very different while still maintaining a lot of the same.

they're not top of the charts but i enjoy gradius v, auto modellista, xiii, and dynasty warriors 4.

more popular games might be shadow of the colossus, tony hawk pro skater 3, metal gear solid 2, gta, etc. i'm not real into those except the first one but they got good ratings.

Neopets: The Darkest Faerie is a surprisingly good action RPG made by a dev team that wanted to push the Neopets franchise into more of a "young adult" territory.

Not a single Ace Combat mention, how disappointing. AC 5 and Zero awe absolute musts. I also recommend Mercury Meltdown Remix, and Midnight Club 3 Dub Edition Remix. Honorable mentions include Burnout Revenge, Lego Star Wars, Treasure Planet (I might be biased shut up), and Atelier Iris 3: Grand Phantasm.

One that's rarely mentioned anywhere but that's a lot of fun even today is The Lord of the Rings: The Third Age. Especially if you like the franchise but it's also a solid game as is. It's a turn based rpg and you're kind of playing through the main story of lotr but you control a party of 6 characters that don't appear in the movies and kinda have their own battles to fight.

There's plenty of lists online that'll give you a good rundown of the popular ones, but my absolute favorite is a hidden gem called Steambot Chronicles. It's got so many different things to do packed into it, from fighting with giant customizable robots to playing a bunch of instruments with unique rhythm mechanics, to hustling pool. Plus the storyline splits based on dialogue choices you make, leading to a few different endings including a couple where you join the bad guys. It's just a really fun game that I've played more times than I can count.

SSX tricky, battlefront 1-2, sly cooper