First of all... If you live anywhere alse than America or Japan, don't bother. The pal territories got the low end of the stick. The 50hz aren't always an issue, as most games where it matters often give you the option to choose between 50hz or 60hz (and some times even progressive scan).
The real issue is the
region coding. We've missed tons of games here, especially Jrpgs that looked more animeish that they should. To give you an example, the first Tales game game to release on a EU sony console was Tales of Graces F. You will be better off using emulators or importing your console from the US.
Once you solve the region problem (if you had any) then taking into account and
excluding those who have recent good remasters, I suggest the following.
_______________________________
Starting with horror:
Silent Hill 2, 3.
The legendary series of horror. The 3rd isn't as good as the 2nd but it's still good.
Fatal Frame/Project Zero 1, 2 & 3.
The actual scariest games on the ps2. The us version of the first game had an atrocious cover but they've learned after that. After those 3, they've jumped to Nintendo consoles, and like most other PlayStation IPs that jumped ship they fell to obscurity, forcing motion controls into the game, falling back graphically, making all characters look like Idols and abandoning the fixed cinematic cameras for "behind the back" ones. The ps2 was the golden age of the series.
Haunting Ground.
Originally intended to be Clock Tower 4, it's changed its brand after the failure of the 3rd. It's a shame, because they improved the formula in every single aspect. The direction remained trippy, the pursuers are now themed around rapists (though they don't explicitly tell it) the pursuing mechanics where massively improved, there are tons of secrets and unlockables and you have a good boy helping you.
Now lets go to RPGs:
Dark Cloud 2/ Dark Chronicle.
The first game didn't age very well, but the sequel is so much better and independent so you shouldn't care.
Xenosaga trilogy.
I haven't played them (living in Europe) but if you ask anyone who did, he'll tell you that they are among the best! The remasters have been recently confirmed to be cancelled, so go nuts!
Tales games.
There are tons of them. Sadly, once again they never reached pal territories, nether got remastered, so I can't tell my self about them.
Shadow hearts trilogy.
Taking place on the same universe as Koudelka (ps1 rpg horror) it's one of the best rpgs the console could offer. The 1rst is a bit old and the 3rd has a more independent story, but their quality remains.
Wild Arms 3, 4 & 5.
I'll just say one thing. "Wild west inspired Jrpg..."
Breath of Fire: Dragon quarter.
This one is a bizarre and polarizing game in the series. It was made to require a restarting of playthrough. If you are hard core enough you can try it.
Persona 3 fes.
The 4rth game got a fantastic remaster on the Vita, but this one didn't get a proper one. The psp remaster improved many gameplay aspects, but essentially removed most of the graphics. This ps2 version is the last edition with graphics.
Grandia 3.
It's not the best in the series, but it's still good, and the ps2 is the only place you can find it. Don't bother with Grandia 2. It's ps2 port is horrible!
Suikoden 3 & 5.
S3 is a bit old but it checks out. S5 is a bit rare, but if find the means to play it it's among the best. Don't bother with S4 or tactics unless you are a hardcore fan.
Dragon Quest 8.
The first DQ game to reach Europe, and with good reasons. They've put lots of effort on this one!
Grimmgrimoire.
It's a Vanilaware game!
Growlancer games.
Anyone you can find. Their releases outside of Japan are very spotty.
Rogue Galaxy
The story is an obvious Star Wars rip-off, but this is one RPG very well made! One of the last JRPGs to hit the PS2, it shows all the lessons they've learned. It's also available on PSN for the PS4 with various graphical enhancements, but as I said, Digital-only don't count, and therefore it's on this list.
Star Ocean: Till the end of time!
The 3rd game in the series, and it clearly had a lot of work put into it. In Japan it had a massive accident, where the devs relied on an aspect of PS2 that didn't exist in the newer models making unplayable forcing a recall and it gathered lots of negative press (needless to say ours is the fixed edition). In actuality, the game is huge, with very good action combat, two disks worth of story. Just remember that like all previews Star Ocean games until that point, the majority of the game takes place i a medieval planet.
Valkyrie Profile 2
The prequel to the PS1 Valkyrie Simulator, this one simplified some of it's aspects, (some for the better, some for the worse) but it's undeniably a more polished game. Since it's a prequel, you don't need to have played the first game.
Other games:
Ape escape 2 & 3.
Kojima's continuation of the gimmick series.
Klonoa 2. Lunatias Vail.
The only sequel in this underrated series.
Rayman Revolution & 3.
The ps2 version of R2 is unique, with exclusive stages, a hub world and voice acting. Not all changes are for the best (namely the voice acting), but it's worth a look!
Indigo Prophesy/ Fahrenheit.
The game that started the interactive movie trend.
Guilty Gear X, XX reload & XX accent core plus.
One of the best fighting game series. XX reload and Accent core plus are technically the same game, but they have enough changes to justify the extra purchase (including a new story).
Samurai Shodown Anthology.
It has them all! Especially the US version that has V special that had fatalities.
Gregory Horror Show.
It's "Hotel California" the game! It's graphics are weird but don't let them fool you.
Beyond good and Evil
One of Ubisoft's most underrated games! I don't know what drove people off, my money are on the color palette. There is a remaster on PS3, but it's digital-only and for me it doesn't count.
Shinobi & Nightshade/Kunoichi
Just like the past with Nintendo and Sega, this is the Ninja gaiden of the Sony consoles. The Shinobi series went for a reboot on the PS2, and they brought a new slicing mechanism to justify it. The action is fast, and the game encourage you to play even faster and it's generally one of the hardest games on the console! The sequel, known as Nightshade in the west, ditched the stressful life drain for aerial combat (which is even more stressfull).
Time Splitter series.
I had little faith that an FPS could be done well on a console, until I played this game. Made from the same team that made Golden Eye, every aspect of it's FPS is designed for consoles from the get go. It has all the necessary tools for a fantastic local multiplayer, including tons of modifiers, tons of models, tons of stages, a level editor and co-op on every single story mission!
Mister Mosquito.
Here is a weird one... You are a mosquito! Your job is to land in various hot-spots of a family's bodies and suck their blood without them figuring you out.
Musashi Samurai Legend
A sequel/reboon of Brave Fencer Musashi. This one was made by nomura, and he brought all his quorks we've later seen in kingdom hearts. While it apparently lost some of it's charm and color from the original, this is still a very polished game!
Transformers
This one is surprisingly good for a licenced game! You control one of 3 transformers in big maps, changing between car and robot on the fly, and finding/using special add-ons to modify their play!
Summoner
The first game is old, and the second game isn't nearly as good. This is a somewhat decent Western RPG for you to try.
Those are the ones that immediately come to mind.
There are plenty more, but they have already been been remastered or remade.
Consider this a hint and check all those remaster.