For the specific games being sold on the PSN, yeah. The actual discs are a different story. Google the details. Nope, they're wrapped in DRM just like any other console software.

The PS1 and the PSP had some of the best exclusive JRPGs ever (most were developed by Square Soft). Below is a list of some my favorite ones plus some other game genres for both systems.

PS1 JRPGs:
Final Fantasy Origins [includes: FFI & FFII]
Final Fantasy Chronicles [includes: FFIV & Chrono Trigger]
Final Fantasy Anthology [includes: FFV & FFVI]
Final Fantasy VII
Final Fantasy VIII
Final Fantasy IX
Chrono Cross
Star Ocean: The Second Story
Xenogears
Vagrant Story
Parasite Eve 1 & 2
The Legend of Dragoon

PS1 Tactical JRPGs:
Final Fantasy Tactics
Front Mission 3

PS1 Survial Horror:
Resident Evil 1, 2, & 3
Silent Hill

PS1 Action Platformers:
Spyro 1, 2, & 3
Crash Bandicoot 1, 2, & 3
Wild 9
Oddworld: Abe's Exodus
Castlevania: Symphony of the Night

PS1 Tactical Espionage Action:
Metal Gear Solid

PSP JRPGs:
Crisis Core: Final Fantasy VII
Final Fantasy IV: The Complete Collection [includes: FFIV & FFIV:After Years]
Final Fantasy Type-0 [note: Import from Japan. Japanese language only]
Final Fantasy I & II

PSP Tactical JRPGs:
Final Fantasy Tactics: The War of the Lions (PSP remake of Final Fantasy Tactics for PS1)
Tactics Ogre: Let Us Cling Together

PSP Action RPGs:
Kingdom Hearts: Birth by Sleep
The 3rd Birthday (sequel to Parasite Eve 2)

PSP Action Platformers:
God of War Ghost of Sparta
God of War Chains of Olympus

PSP Tactical Espionage Action:
Metal Gear Solid: Peace Walker
Metal Gear Solid: Portable Ops

PSP Fighting RPGs:
Dissidia 012 Final Fantasy

Breath of Fire III (PSP version of the original PS1 version) which should be out now in the US finally I think.

Blood Omen: The Legacy of Kain, though I don't know if it works on Vita.

I came here to say this. Judas, you have good taste there.

You can't download it on Vita through the American store, but you can do so through the European store.

Ah I see, don't have any newer Sony consoles or portables so I wasn't sure.

Persona 3 is my favorite game of all time, it eschews common fantasy settings and tropes and instead goes for something more grounded, well written characters with everyday problems, with just a smidge of magical realism sprinkled on top. I guarantee, if you haven't experienced any of the Shin Megami Tensei games, Persona 3 is the best place to start, and it will be like nothing you have ever played. Plus, the PSP version is the best version of the game, incorporating gameplay improvements from Persona 4 and with the largest amount of content.

A lot of people here are blindly recommending games they think are good, without taking into account the platform you'll be playing on. If the emulated versions on Vita are just like the PS1 originals, you must stay as far away as possible from Chrono Trigger, Final Fantasy 4, and any other game that was ported from the SNES to the PS1.

I played CT in the PS1 and the loading times are atrocious. It took 3 to 5 seconds loading every time I went to the menu. You can find better versions of those games elsewhere.

The way I see it:

6 had many aspects, some good (the non-linear second half of the game), some bad (the excessively long cutscenes).

7 took the bad aspects of FF6, threw away the good aspects, and made a few other negative changes (like reducing the party size).

Also, 3 on the SNES is 6, not 5.

Of note (aside from the fact that FF7 should be avoided):
Final Fantasy Origins has the best version of FF1, but the worst English version of FF2. (I actually consider Origins FF2 to be worse than the Famicom version; they actually made spell leveling even slower!)

Final Fantasy 1 PSP isn't a good version because it's based off the GBA version, which ruined the game balance and any difficulty the main game had. Final Fantasy 2 PSP, on the other hand, is a good version of that game; it's based off the GBA version, which had many improvements, including having spells actually, for once, level up at a good speed.

FF4 PSX doesn't have any issues except for the long time it takes to save/load; once you're in the game, it runs quite smoothly. Also, as I mentioned, it is the closest to the original of all the offical English versions.

FF5 and FF6 have issues with the sound quality being rather poor, but are at least reasonably playable despite that. (Also, FF6 PSX is the only official English version where Gau can dual wield while still equipping the Offering, thanks to a glitch.)

I'd say that all Final Fantasies should be played in their original form, not their remakes.

Also I agree, FF 5 on PSX was horrible with long loading times everywhere + totally non-canon translation.

I wouldn't say that FF 7 was that bad, it had its issues, but it was a much more polished game than FF 6 and it was the first game to introduce true FF Superbosses (Omega and Shinryu in FF V don't count). FF 9 is also not bad game.

But FF 8... it is better to avoid it at all costs. Nothing in that game makes sense whatsoever.

As always, it's a matter of taste.
FF 8 was by far my favourite FF (I only played 1, 6, 7, 8, 9).
But then, I often don't make any sense whatsoever either.

I disagree. Omega and Shinryu do count. Furthermore, it was definitely not more polished than FF6; the graphics look considerably worse, load times are considerably worse than in FF6 SNES, and who thought Knights of the Round was balanced? (It's far worse, from a balance perspective, than FF6 Ultima.) Also, the minigames were clearly not polished and also felt like they did not belong in an RPG.

You should play FF5; it is by far the best in the series. (While you're at it, also play 2, 3, and 4; since you liked 8, you might like 2, which is probably about as balanced as 8 is, anyway.)

Unlikely to happen any time soon. Already sold my entire PSX collection and haven't bought any non-GOG game in the last 5 years or so. Unless GOG begins to sell emulated console games, that is.

But they had much lower endurance than that of the final boss. They were more like glass cannons, while actual superbosses have endurance far exceeding that of storyline bosses.
Graphics had specific "super deformed" style, which could scare away some people, but otherwise they are fine. Akso you weren't getting KotoR until the very end of the game, and even then you should know where to find it. FF 6 gave you Atma (Ultima) Weapon in 1st World in a place, it is hard to skip it, and it allowed you to do 9999 damage so early on. There was only one truly mandatory minigame in FF7, the rest could be skipped or completed/failed in whatever careless way. It was FF8, which threw one obnoxious mini-game on you after another, while heavily punishing you for playing actual game.

FF 7 was much bigger in scope, it didn't have absurd level-up mechanics (like with Espers in FF6), it didn't have such big bugs like FF6 had and FF7 actually provided some challenge... sometimes... but still more than FF 6. Also Sephiroth is quite an attractive character, some players, men and women alike, even had a crush on that virtual anti-hero. And who is Kefka? Just some clown? If to speak about megalomaniacs, Queen Brahne from FF IX was a much more interesting character.

Corpse Party and CP: Book of Shadows I would definitely recommend.
Don't ever bother with Blood Drive unless it gets a console/PC release.