There's quite a few RPGs on the PSP, but the best ones are ports:
(Stolen from Digital Press)
Adventures To Go (Dev. Global A, Pub. Natsume, 10/27/2009)
Aedis Eclipse: Generation of Chaos (Dev. Idea Factory, Pub. NIS America, 4/24/07)
Astonishia Story (Dev. Sonnori, Pub. Ubisoft, 6/6/06)
Blade Dancer: Lineage of Light (Dev. Hit Maker, Pub. NIS America, 7/18/06)
Brave Story: New Traveler (Dev. Game Republic, Dev. XSeed Games, 7/31/07)
Breath of Fire III (Dev. Capcom, Pub. Capcom, 2/10/06) *Europe release
Class of Heroes (Dev. Zerodiv, Pub. Atlus, 6/9/09)
Crimson Gem Saga (Dev. Matrix, Pub. Atlus, 5/26/09)
Crisis Core: Final Fantasy VII (Dev. Square Enix, Pub. Square Enix, 3/24/08)
Disgaea: Afternoon of Darkness (Dev. NIS, Pub. NiS America, 10/30/07)
Disgaea 2: Dark Hero Days (Dev. NIS, Pub. NIS America, 9/8/2009)
Dragoneer's Aria (Dev. Hit Maker, Pub. NIS America, 8/21/07)
Dungeons & Dragons Tactics (Dev. Kuju Entertainment, Pub. Atari, 8/14/07)
Dungeon Explorer: Warriors of Ancient Arts (Dev. Hudson Soft, Pub. Hudson, 2/15/08)
Dungeon Maker: Hunting Ground(Dev. Global A, Pub. XSeed Games, 6/19/07)
Dungeon Maker II: The Hidden War (Dev. Global A, Pub. UFO Interactive, 12/9/08)
Dungeon Siege: Throne of Agony (Dev. SuperVillian Studios, Pub. Take-Two, 10/30/06)
Final Fantasy (Dev. Square Enix, Pub. Square Enix, 6/26/07)
Final Fantasy II (Dev. Square Enix, Pub. Square Enix, 7/24/07)
Final Fantasy Tactics (Dev. Square Enix, Pub. Square Enix, 10/09/07)
Generation of Chaos (Dev. Idea Factory, Pub. NIS America, 2/28/06)
Half-Minute Hero (Dev. Marvelous, Pub. XSEED, 10/13/2009)
Harvest Moon: A Boy and A Girl (Dev. Marvelous, Pub. Natsume, 7/31/07)
Harvest Moon: Hero of Leaf Valley (Dev. Marvelous, Pub. Natsume, 4/20/10)
Hexyz Force (Dev. Sting, Pub. Atlus, 5/25/10)
Innocent Life: A Futuristic Harvest Moon (Dev. ArtePiazza, Pub. Natsume, 5/15/07)
Jeanne D'Arc (Dev. Level 5, Pub. SCEA, 8/21/07)
Justice League Heroes (Dev. Snowblind Studios, Pub. Warner Bros., 11/22/06)
Kingdom of Paradise (Dev. Climax Entertainment, Pub. SCEI, 11/15/05)
Legend of Heroes: A Tear of Vermillion (Dev. Falcom, Pub. Bandai, 11/15/05)
Legend of Heroes II: Prophecy of the Moonlight Witch (Dev. Falcom, Pub. Namco Bandai, 6/20/06)
Legend of Heroes III: Song of the Ocean (Dev. Falcom, Pub. Namco Bandai, 1/23/07)
Lord of the Rings Tactics (Dev. Amaze, Pub. EA, 11/8/05)
Lunar: Silver Star Harmony (Dev. Game Arts, Pub. XSEED, 3/2/10)
Mana Khemia: Student Alliance (Dev. Gust, Pub. NiS America, 3/10/09)
Marvel: Ultimate Alliance (Dev. Vicarious Visions, Pub. Activision, 10/24/06)
Marvel Ultimate Alliance 2 (Dev. Vicarious Visions, Pub. Activision, 9/15/09)
Mimana Iyar Chronicle (Dev. GungHo, Pub. Aksys Games, 3/30/10)
Monster Hunter Freedom (Dev. Capcom, Pub. Capcom, 5/23/06)
Monster Hunder Freedom 2 (Dev. Capcom, Pub. Capcom, 8/28/07)
Monster Hunter Freedom Unite (Dev. Capcom, Pub. Capcom, 6/26/09)
Monster Kingdom: Jewel Summoner (Dev. Gaia, Pub. Atlus, 2/19/07)
Mytran Wars (Dev. Stormregion, Pub. Deep Silver, 10/20/09)
Neverland Card Battles (Dev. Idea Factor, Pub. Yuke's Company of America, 10/27/08)
Persona (Dev. Atlus, Pub. Atlus, 9/22/09)
Phantasy Star Portable (Dev. Alfa System. Pub. Sega, 3/3/09)
Popolocrois (Dev. G-Artists, Dev. Agetec, 11/29/05)
Puzzle Chronicles (Dev. Infinite Interactive, Pub. Konami, 2/2/10)
Puzzle Quest: Challenge of the Warloads (Dev. Vicious/Infinite, Pub. D3, 3/20/07)
Riviera the Promise Land (Dev. Sting, Pub. Atlus, 7/11/07)
Silverfall (Dev. Monte Cristo Multimedia, Pub. Atari, 8/3/07) *Europe release
Spectral Souls (Dev. Idea Factory, Pub. NIS America, 9/26/06)
Star Ocean: First Departure (Dev. TOSE, Pub. Square Enix, 10/21/08)
Star Ocean: Second Evolution (Dev. TOSE, Pub. Square Enix, 1/20/09)
Tales of Eternia (Dev. Namco, Pub. Ubisoft, 2/10/06) *Europe release
Tales of the World: Radiant Mythlogy (Dev. Alfa System, Dev. Namco Bandai, 7/17/07)
Untold Legends: Brotherhood of the Blade (Dev. Sony Online Entertainment, Pub. Sony Online Entertainment, 3/22/05)
Untold Legends: The warrior's Code (Dev. Sony Onine Entertainment, Pub. Sony Online Entertainment, 3/28/06)
Vahalla Knights (Dev. K2 LLC, Pub. Xseed, 4/17/07)
Vahalla Knights 2 (Dev. K2, Pub. Xseed, 10/1/08)
Valhalla Knights 2: Battle Stance (Dev. K2, Pub. XSEED, 1/21/10) *Digital Download only
Valkyrie Profile: Lenneth (Dev. Tri-Ace, Pub. Square Enix, 7/18/06)
Warriors of the Lost Empire (Dev. Tommo, Pub. UFO Interactive, 12/13/07)
Wild Arms XF (Dev. Media Vision, Pub. Xseed, 3/11/08)
X-Men Legends II: Rise of Apocalypse (Dev. Vicarious Visions, Pub. Activision, 10/18/05)
Yggdra Union(Dev. Sting, Pub. Atlus, 9/16/08)
Ys: The Ark of Napishtim (Dev. Falcom, Pub. Konami, 2/28/06)
Undecided (7)
Dissdia: Final Fantasy (Dev. Square Enix, Pub. Square Enix, 8/25/09)
Gurumin (Dev. Falcom, Pub. Mastiff, 2/12/07)
Metal Gear Acid (Dev. Konami, Pub. Konami, 3/22/05)
Metal Gear Acid 2 (Dev. Konami, Pub. Konami, 3/21/06)
Prinny: Can I Really Be the Hero? (Dev. NIS, Pub. NIS America, 2/17/09)
R-Type Command (Dev. Irem, Pub. Atlus, 5/6/08)
Steambot Chronicles (Dev. Irem, Pub. Atlus, 6/30/09)
Non-US English Releases (3)
Breath of Fire III (Dev. Capcom, Pub. Capcom, 2/10/06)
Silverfall (Dev. Monte Cristo Multimedia, Pub. Atari, 8/3/07)
Tales of Eternia (Dev. Namco, Pub. Ubisoft, 2/10/06)
Compilation (3)
Castlevania: Dracula X Chronicles [Castlevania: Symphony of the Night] (Dev. Konami, Pub. Konami, 10/23/07)
EA Replay [Ultima VII] (Dev. Team Fusion, Pub. Electronic Arts, 11/14/06)
Sega Genesis Collection [Phantasy Star II, III, and IV] (Dev. Sega, Pub. Sega, 11/16/06)
Upcoming Releases
Final Fantasy Agito XIII (Dev. Square Enix, Pub. Square Enix, ????)
God Eater (Dev. Bandai Namco, Pub. D3, Q3 2010)
Kingdom Hearts: Birth by Sleep (Dev. Square Enix, Pub. Square Enix, 9/7/10)
Knights in the Nightmare (Dev. Sting, Pub. Atlus, 10/19/10)
Legend of Heroes: Trials of the Sky FC (Dev. Falcom, Pub. XSeed, 2011)
Legend of Heroes: Trials of the Sky SC (Dev. Falcom, Pub. XSeed, TBA)
Legend of Heroes: Trials of the Sky TC (Dev. Falcom, Pub. XSeed, TBA)
Parasite Eve: The 3rd Birthday (Dev. Square Enix, Pub. Square Enix, ????)
Phantasy Star Portable 2 (Dev. Sega, Pub. Sega, 9/28/10)
Persona 3 Portable (Dev. Atlus, Pub. Atlus, 7/6/10)
Puzzle Quest: Galactix (Pub. D3 Publisher, ????)
Valkyria Chronicles 2: The Royal Military Academy (Dev. Sega, Pub. Sega, 10/5/10)
Ys I & II Chronicles (Dev. Falcom, Pub. XSeed, 2011)
Ys VII (Dev. Falcom, Pub. XSeed, Q3 2010)
Ys: Oath in Felghana (Dev. Falcom, Pub. XSeed, 2010)
Jean De' Arc is said to be good, the Star Ocean remakes are very good too. I can also recommend Legend of Heroes games are straightforward, but are fun, and the rest are coming next year.
On the horizon, we have Ys games coming this and next year, and Knights in the Nightmare is coming in Oct.
Hexyz Force is another game I'd recommend.