Note: All games unless otherwise noted are turn-based.
Dungeons & Dragons: Tactics
Jeanne d'Arc
Warhammer 40K: Squad Command
Disgaea: Afternoon Of Darkness
Dragoneer's Aria
Dungeon Maker: Hunting Ground
Final Fantasy I
Final Fantasy II
Rivier: The Promised Land
Final Fantasy: Tactics: The War Of The Lions
Field Commander
The PSP has many other types of games available, including many PSOne ports, but I wanted to post mainly about the turn-based goodness for now. You can download and run any PSOne game's .ISO on a hacked PSP, by the way, so it really is a "Playstation Portable". Unfortunately the PSP doesn't have very many games that could be considered unique or original, unlike the DS which has games like Trauma Center and Pheonix Wright.
Dungeons & Dragons: Tactics
Dungeons & Dragons Tactics is a tactical role-playing game released on the PlayStation Portable handheld video game console. It is set in the world of Dungeons & Dragons and uses a strict interpretation of the Dungeons & Dragons 3.5 Edition rule set.
In the campaign storyline, players lead a party of adventurers on their quest to investigate an ancient being, about which little beyond the name is initially known. The plot is eventually revealed to be an epic contest between two dragons competing for godhood. The player can choose the path of good or evil, with different quests available depending on which is preferred, although the distinction between the two is not always clear. The game is divided up into a number of distinct battles or missions (30+), with the player able to access the majority of these during a given campaign, since several of the scenarios are mutually exclusive. Scenarios cannot be re-played once successfully completed.
Jeanne d'Arc
Jeanne d'Arc is a tactical role-playing game developed by Level-5 and published by Sony Computer Entertainment for the PlayStation Portable. It is Level-5's first RPG of this kind, as well as the studio's first production on the PlayStation Portable. The title's narrative makes use of various fantasy elements, and is loosely based on the story of Joan of Arc and her struggles against the English occupation of France during the Hundred Years' War in the early 15th century.
The game has an amount of historical accuracy when it comes to the cast of characters, and contains many who were real world contemporaries and allies of Joan of Arc. This contrasts starkly with the many fantasy elements of the game. These include Jeanne and four other main characters possessing magical armlets that give the wearer special abilities, and suggesting that King Henry VI of England was possessed by demons and using them to aid his armies in destroying France during the Hundred Years' War.
Warhammer 40K: Squad Command
Squad Command uses a unique turn-based gameplay system to mimic the play of the tabletop wargame. It features fully destructible 3D environments and over 20 weapons to utilize, such as the bolter and powerfist. According to THQ, Squad Command will fully make use of the two platforms portable functionality, including the DS's dual screens and stylus controls.
Squad Command uses Hit Points (HP) and Action Points (AP). Hit Points are used to calculate damage to a unit, when a unit's HP hits zero they die and are removed from the battle. Action Points are expended when the unit moves or fires a weapon. Movement uses any number of AP whereas weapons have a minimum amount allowable, the player can increase accuracy by increasing the amount of AP used whilst firing.
If a unit still has enough AP to fire their weapon after a turn of combat they enter "Overwatch" mode in the enemy turn. In Overwatch any enemy unit that enters the Overwatch unit's line-of-sight is fired upon. Some heavy weapons (such as Sniper Rifles or Plasma Guns) lower the amount of AP a unit may use in a turn.
Disgaea: Afternoon Of Darkness
A port for the PlayStation Portable named Disgaea Portable was released in Japan on November 30, 2006. It was later released in the United States on October 30, 2007 under the name Disgaea: Afternoon of Darkness.
In addition, Afternoon of Darkness includes a complete dual language option and the option to turn off battle animations, both of which have been included in recent Nippon Ichi games such as Disgaea 2 and Soul Nomad. Most of the cut scenes that were originally voiceless now include voices, though some of cut scenes are still voiceless. To reflect Etna's recent voice actor change, her lines have been re-recorded to match Michelle Ruff's portrayal of Etna in Disgaea 2 and the anime. Also, voice acting for the Prinny classes have been removed from the PSP port however.
Dragoneer's Aria
The game features a turn-based battle system, and enables the player to select the order in which the characters are to act. The actions that a character can make during battle are "Attack" (enables the character to physically attack an opponent), "Mana" (enables the character to perform skills and magic), "Guard" (allows the character to defend against an opponent's attack), "Item" (allows the character to use an item in the inventory), and "Escape" (allows the characters to run away from battle).
Magic is performed through attaching jewels called "lusces" to accessories such as rings and necklaces. The strength and effectiveness of lusces and other skills are improved through repetitive use; the more often skills and lusces are used, the more powerful they become.
Dungeon Maker: Hunting Ground
In an effort to protect a small town from attacks by monsters and demons, a novice "dungeon maker" has decided to create a dungeon in a nearby cave in order to lure the monsters away from the town itself. Conceptually, the hope is that such creatures will find the dungeon appealing and hence settle there, rather than roaming about. The dungeon architect can then venture into the dungeon and exterminate them.
As the dungeon grows larger and deeper, more powerful foes are expected to take up residence. Ultimately, the dungeon maker (played by the player) intends to attract a legendary foe, the "Wandering Demon", whose defeat will hopefully lead to long-term peace for the region.
Final Fantasy I
The PSP version has higher-resolution 2D graphics, the FMV sequences from the Origins release and the bonus dungeons from the Dawn of Souls release. It also borrowed the soundtrack from the Origins release, though the extra dungeon boss battles use the music that was used in the game they originated from (e.g Gilgamesh's music from Final Fantasy V while fighting Gilgamesh), and the gameplay from the Dawn of Souls release. The PSP version has aerial effects on the towns and dungeons. Mode 7 is used on both the walking and airship parts. It also contains an all-new dungeon, as well as an Amano Art Gallery. The gallery uses the PSP's high resolution to display high-quality art by Yoshitaka Amano, with new pieces of art being unlocked as the player progresses through the game.
Final Fantasy II
First revealed by Japanese magazine Famitsu on January 17, 2007, the PSP remake features improved graphics, the FMVs from Final Fantasy Origins, and the bonus quest and dungeons from Final Fantasy I & II: Dawn of Souls. It also includes the 'Arcane Labyrinth' and 'Arcane Sanctuary' dungeons, exclusive to this version, in which character-specific equipment can be found (even for temporary characters, and separate from the Soul of Rebirth equipment), alongside powerful enemies and a new boss. Depending on actions taken on this boss, the player can obtain one of two Tomes containing the most powerful of white and black magic spells (aside from Ultima): 'Revive' and 'Destroy' (respectively).
Rivier: The Promised Land
Riviera is a turn-based RPG game, with some elements from strategy and dating sim games. The last aspect manifests itself in the conversation in the game. Often, Ein will have to favor either Fia, Lina, Serene or Cierra over the others in scenes in which the characters interact with each other. This affects their trust for Ein, and their mood, and eventually the game's outcome.
For each of the seven main chapters of the game, the player starts in Elendia, and is given a mission. The player then moves on to wherever that mission takes place, proceeding through nine areas, to the eighth area which will contain the chapter boss. The ninth area is secret, and often has a particular method of infiltration. Within each area are multiple screens, all with events and battles of their own. When a chapter is completed, all trigger points currently accumulated are erased, and the player is taken to a results screen showing how they performed in the chapter, and gaining trigger points based on that performance that can be used in the next chapter.
Final Fantasy: Tactics: The War Of The Lions
Final Fantasy Tactics: The War of the Lions is a tactical role-playing game developed by TOSE and published by Square Enix for the Sony PlayStation Portable handheld game console. The game is an updated version of Final Fantasy Tactics for the PlayStation video game console.
Field Commander
Field Commander is a military turn-based strategy game for the PlayStation Portable set in the modern era. It has many similarities to Nintendo's Advance Wars games. The player takes on the persona of a new recruit to ATLAS (Advanced Tactical Legion for Allied Security), a world alliance of military technology and expertise. The player battles Shadow Nation, a crime empire, on various missions.
The multiplayer options include Infrastructure, Ad-Hoc, Hot Swap, and a unique feature called Transmission mode, which is somewhat similar to the Play By Email system of older PC games. While playing in Transmission mode each player takes turns and sends them off to the server.
The PSP has many other types of games available, including many PSOne ports, but I wanted to post mainly about the turn-based goodness for now. You can download and run any PSOne game's .ISO on a hacked PSP, by the way, so it really is a "Playstation Portable". Unfortunately the PSP doesn't have very many games that could be considered unique or original, unlike the DS which has games like Trauma Center and Pheonix Wright.