I have a few games in mind:
Dark Cloud Series - Dark Cloud 1 and 2 are my favorite RPGs on the PS2 and they were also unique for their time. Even though Dark Cloud 1 was straightforward and didn't have any side quests or other things to do besides fishing and dungeoning, the post endgame dungeon helped somewhat with it's replay value and it's still fun to play from scratch. With Dark Cloud 2, there were many other things to do such as recruit important people to your villages, participate in various contests, take pictures of various things, then combine ideas to create new items, and more. Also the Georama constructions of towns allowed more freedom compared to the first game and I remember spending a good hour or two trying to make my villages look better. Though, what both games had which made it stand out from other RPGs was it's unique weapon system. In the first game you were able to combine crystals, stones, and gems to power up your weapon, and depending on the attributes it had, you were able to transform it into an entirely new weapon. You could also "Synthesize" your weapon to combine some of it's stats and skills with another weapon to create a more powerful one. The second game took this step even further by allowing almost any item to be used to power up your weapons with different effects. They also had many more attributes to choose from, however you were limited to what you could use with your weapon depending on it's level unlike the first game. There were many other decent concepts as well from both games, but their storyline was too plain.
I know Level-5 and SCE Japan Studio still exist today, and I would love to see them create a third installment for the game or even a fresh reboot of the series.
Dino Crisis Series - These PSOne classics were very unique and although it had similar features like Resident Evil, the main difference was dinosaurs instead of your traditional zombies and other infected creatures. Even though it was no where near the level of "scary" as classic RE titles, it still provided interesting gameplay.
What I would love to see is Capcom creating a fresh start for the series. I would like the game to actually be scary, and have a good balance between action and horror (Think Dead Space) and not become a complete action game with very little horror elements. (Resident Evil 6 *COUGH*)
The Legend of Dragoon - Now this RPG is a classic example of a great PSOne title. It had a good storyline, interactive gameplay, and was not a Final Fantasy game. If you have even heard about this or played it, I won't have to explain why I would want a sequel or a fresh installment to this game.
Mystic Heroes - Don't let the title throw you off, this game was actually a very fun game to play, whether it was with your friends or alone. The storyline and voice acting was terrible, but the gameplay is basically the same as any other Dynasty Warriors game.
Gauntlet Series - Gauntlet and Gauntlet Legends will forever be by favorite arcade and console games of my childhood. If you ever played this game or seen it, you would know how fun this game is. With friends, the game is much more exciting, especially if you're trying to play on a competitive scale and everyone is fighting for food. (the wizard will ALWAYS need food badly!) The PS2 installment was terrible, and it completely ditched the formula that made the previous installments such amazing arcade games. If it's an arcade game, keep it that way. Don't try to remake it into a console style RPG.
Galarians - This sci-fi survival horror game was probably the most difficult PSOne game I ever played. Careful management of your superpowers is valuable, and wasting it can easily lead to your death. I never actually played the game from start to finish, but I have seen my cousin play it enough to know my way around and to be familiar with the controls and gameplay. I wouldn't mind seeing a second entry to this game.
Star Ocean Series - This game is overdue for a new entry. The past Star Ocean games have been very good, despite The Last Hope getting mixed or poor reviews. (my favorite will always be Till the End of Time) If you are familiar with any of the Star Ocean games, then you know how good the gameplay is for an RPG.
Infinite Undiscovery - Developed by Tri-Ace, the same developers of the Star Ocean Series, this 360 exclusive was a very good game. It had gameplay similar to Star Ocean in a way but was simplified, and like traditional Tri-Ace games, it had it's trademark post game bosses and dungeons.
Shadow Hearts Series - This RPG had a good storyline and a unique battle system which involved a Judgement Ring. There was two additional entries after the first, but they received much criticism, and the first one is more well-known. I don't see this game ever being revived, since the original publisher Sacnoth dissolved and became a part of Marvelous AQL, however I would love to see a fresh restart for this amazing game series.
Digimon World 4 - The reason why i'm singling out this game and not talking about the entire franchise is because this game was completely different from the rest, and Digimon games tend to be completely different with each newer installment. instead of following the usual gameplay formula, Bandai tried something new and created a 4 player co-op world with four main areas, many dungeons to explore, many side quests to do, NG+ with two higher difficulties, and plenty of loot to find. Yes, I said loot, because this game allowed you to find various items and equipment for your Digimon and allowed you to specialize in specific techniques such as Slash for equipping stronger swords, or Force for using more powerful offensive MP Techniques. You are even allowed to digivolve into different Digimon by completing various tasks. Even though this game is a simplified RPG, it works very well.
Digimon World DS/Dawn/Dusk - This game followed a similar formula to Pokemon, but used a different battle system found in most turn based RPGs. It also allowed you to have your very own Digimon Farm, where you could decorate it with goods and other items to help train your Digimon while you are doing something else. With decent online play, trading, and gameplay, it has potential to be polished into a much more complex game.