I second this. It's probably a good starting point to I think

Can't believe no one said this yet, but if you're going for PSP then try FF6 of Chrono Trigger. They're pretty much the quintessential SNES JRPGs.

I agree with this.

And this is awesome:

http://www.youtube.com/watch?v=PsL_8Xne_Cg

I would recommend Persona 3 or Persona 4. The latest generation of Pokemon games would also be good if you have a 3DS.

breath of death VII
and Cthulhu saves the world!

Have to look more of these vids :D
Yeah, monster hunter has the best...monsters....
You should look up the japanese trailer for Monster Hunter 4 though Monster Hunter 3 Ultimate isn't out yet it doesn't hurt to have a look, the monsters interact with the environment more so there's spider and monkey type monsters.

If by J-RPG you mean what is generally considered a J-RPG and not just any RPG from Japan, I would recommend Chrono Trigger to get into the genre. It's a pretty good game and avoids the nasty traps J-RPGs tend to fall into.

The first thing is that CT is a very fast game, there are no random encounters, no separate battle screens, no summoning animations that last forever. Your guy walks around the maps and so do the monsters, if you touch a monster everyone gets in position and the turn-based fight starts right where you are, no transition. Animations are fairly quick and even spells have an OK length. I like the story because the writers had the brilliant idea of not letting the main character talk, so there won't be any brooding emo-BS to sit through. Don't make false assumptions though, there is a story in the game, but it is told through events and places rather than endless dialogues. The other characters do talk, but just enough to give them enough character, no one outstays their welcome.

It is still a J-RPG though, so expect the game to be fairly linear in terms of where to go. There is no real choice in leveling your characters either, it's all automatic and you always just buy the best equipment when you can. The only real choice is which characters to use in your party and what skills to use in battle. That's what makes J-RPGs, so it's to be expected. That doesn't mean J-RPGs are just about grinding; although grinding is possible, the proper way to play a J-RPG is as an exercise in resource management, to get through the game with as little grinding as possible (yes, CT can be beat without any grinding, so no time wasted). This may make them look like baby-RPGs, and in a way they are, but it also makes them very fast-paced and the linearity allows the designers to do really crazy stuff with the setting, like the whole time traveling.

I tried the universally acclaimed Final Fantasy VII and I couldn't play it past disc 2. There is nothing really wrong ith the game itself, it's just that everything is soooo slow, the entire reason to play J-RPGs was lost to me. If I'm going to play something slow then I want it to be something I can really sink my teeth into. By jumping to 3D everything gets much slower and there is just no payoff for this loss of speed.

Most of the Snes or Playstation 1 JRPGs are pretty good.
Chronotrigger is my personal favorite of the genre.

Phantasy Star is pretty good. I mostly liked IV, the earlier ones didn't really grab me. But, bear in mind that JRPGs aren't RPGs in any meaningful way other than having evolved from RPGs.

But to appreciate these two to their fullest, you need to understand the tropes that they mock (i.e. standard JRPG tropes).

And I would recommend Chrono Trigger, Final Fantasy 6, 7 (recently re-released for PC) or 9 or Grandia 2 (can be found on PC as well). Easy to get into, and these games also tend to show the strengths of the sub-genre more than the weaknesses.

Try the dragon quest games on the DS.

Chrono Trigger is probably one of the best ones to get into the genre. Overall an excellent game, but also is much less grindy than many jRPGs and the story is reasonably coherent (these two things will often put off people first trying out many jRPGs).

You could do far worse than Dragon Quest VIII: Journey of the Cursed King (for PS2). It should be cheap and it's super fun. If you prefer space, aliens, blaster guns, space-magic-kung-fu, cyborgs, and the like, I'd suggest the first Xenosaga (also on PS2).

If you don't mind an old Genesis game, Phantasy Star 2 is available on a number of services now and is one of the all time most famous ones.

Finally, no matter what anyone says, FF VII sucks ass, if you really must play a FF game, go for FF X.

I've tried to limit myself to games that aren't excruciatingly difficult, there are those if you wish. I'd suggest having a look at the DS library if you want something that will make you want to throw something at the wall while screaming "BULLSHIT!".