I don't have time to narrow the list down to only English or non-port games.
So accept this list the way it is. None of them are casual brain trainings.
7th Dragon
(Cute and lovely RPG by Sega. Surprisingly wonderful soundtrack, both traditional and 8-bit. It will come in English soon.)Advanced Wars: Days of Ruin
Animal Crossing: Wild World
Another Code: Two Memories / Trace Memory
Arkanoid DS
Avalon Code
Bangai-O Spirits
(One of Treasure's finest. A great sequel to the Dreamcast game.)Big Bang Mini
Biker Mice From Mars
(Both a side-scroller and racing game. Visuals are good, controls are great. Fast action.)Black Sigil: Blade of the Exiled
(SNES RPG-inspired game, created by an indie company. Release April 14th, 2009.)Bleach: Dark Souls
(Fighting Game)Bleach: The 3rd Phantom
(Strategy RPG)Bleach DS: Souten ni Kakeru Unmei
(Fighting Game)Blue Dragon Plus
Bokura no Terebi Game Kentei
(You play classic Namco games, and beat different challenges. Very fun! ^^)Bomberman
Bomberman 2
Bomberman Land Touch!
Bomberman Land Touch! 2
Broken Sword: Shadow of the Templars: The Directors Cut
(No voice acting, but it still looks as good as the original game.)Bubble Bobble Revolution
Bubble Bobble: Double Shot
Bust-A-Move DS
Castlevania: Dawn of Sorrow
Castlevania: Order of Ecclesia
Castlevania: Portrait of Ruin
Children of Mana
Chrono Trigger DS
(Everything the PS1 version had, but WAY better. C'mon! You know you want to~ ^w^)Code Geass: Hangyaku no Lelouch
(Don't forget to pick "Yes! My lord!" after you write your name. >v<)Contra 4 / Contra: Dual Spirits
Custom Beat Battle: Draglade
Custom Beat Battle: Draglade 2
Daigasso! Band Brothers
Daigasso! Band Brothers DX
Dengeki Gakuen RPG: Cross of Venus
(Dokuro-chan is in this game, along with other cross-over characters)Densetsu no Stafi 4 / Legend of Stafy 4
Dig Dug: Digging Strike
Disgaea DS
Doki Doki Majo Shinpan
(Touch witches... very pink... >v<)Doki Doki Majo Shinpan 2
(Touch witches the second... now with more white... >v<)Dragon Quest IV: Chapters of the Chosen
Dragon Quest V: Hand of the Heavenly Bride
Dragon Quest VI
Dragon Quest IX
Dragon Quest Monsters: Joker
Drawn To Life
Dungeon of Windaria
Elite Beat Agents
Enchanted Folk and the School of Wizardry
English of the Dead: Zombie Shiki: Eigo Ryoku Sosei Jutsu
(This is House of the Dead, but with a twist: Write English words to kill zombies. ^^)Etrian Odyssey
Etrian Odyssey II: Heroes of Lagaard
Feel the Magic
Final Fantasy Crystal Chronicles: Echoes of Time
Final Fantasy Crystal Chronicles: Ring of Fates
Final Fantasy Fables: Chocobo Tales
Final Fantasy III
Final Fantasy IV
Final Fantasy XII: Revenant Wings
Final Fantasy Tactics A2: Grimoire of the Rift
Fire Emblem: Shadow Dragon
Front Mission
Full Metal Alchemist: Dual Sympathy
Game Center CX: Arino no Chousenjou 2
(I can help with the text-based game)Ganbare Goemon: Toukai Douchuu
(Japan-only)Geometry Wars: Galaxies
Guilty Gear: Dust Strikers
Gyakuten Kenji / Miles Edgeworth: Perfect Prosecutor
Gyakuten Saiban / Phoenix Wright: Ace Attorney
Gyakuten Saiban 2 / Phoenix Wright: Ace Attorney: Justice for All
Gyakuten Saiban 3 / Phoenix Wright: Ace Attorney: Trials and Tribulations
Gyakuten Saiban 4 / Apollo Justice: Ace Attorney
Gyakuten Saiban Jiten
(A dictionary and art gallery for the first 3 games)Harvest Moon DS
Harvest Moon: Island of Happiness
Harvest Moon: Shining Sun and Friends
Henry Hatsworth In The Puzzling Adventure
(Hatsworth: "I do say, this hat sure makes me splendidly younger, won't you agree, my boy?")Heroes of Mana
(If only for the music alone)Hotel Dusk: Room 215
Izuna: The Unemployed Ninja
Izuna 2: The Unemployed Ninja Returns
Jump Super Stars
Jump Ultimate Stars
Kage Densetsu: The Legend of Kage 2
Ketsui Death Label
Kimi no Yusha
(RPG, with cuteness~ By the makers of Doki Doki Majo Shinpan! 
)Kimo Kawa E
(Lots of text, just skip it all and enjoy the artworks and cuteness~ ^^)Kingdom Hearts: 358/2 Days
Kirby Cursed Canvas / Kirby: Power Paintbrush / Touch! Kirby
Kirby Super Star Ultra / Hoshi no Kirby: Ultra Super Deluxe
(PLAY IT AGAIN! >v<)Kirby: Squeak Squad / Kirby: Mouse Attack
Knights in the Nightmare
Legacy of Ys Books 1 & 2
Lucky Star Moe Drill
(Only if you're a fan. It has school-related tasks for you to do)Luminous Arc
Luminous Arc 2: Will
Lunar Knights / Bokura no Taiyo: Django & Sabata
(Now the sun and moon is in your hands)Lunar: Dragon Song / Lunar Genesis
(If you're a fan of Lunar, give it a chance at least)Magical Starsign / Magical Vacation
Mario & Luigi: Partners in Time / Mario & Luigi RPG 2x2
Mario & Luigi RPG 3
Mario Kart DS
Mario Party DS
Mario vs. Donkey Kong 2: March of the Minis
Meccha! Taiko No Tatsujin DS: 7-tsu No Shima No Daibouken
Metal Slug 7
Meteos
Metroid Prime Hunters
Moero! Nekketsu Rhythm Damashii Osu! Tatakae! Ouendan 2
Mr. Driller: Drill Spirits
Mugen no Frontier: Super Robot Taisen OG Saga
(Eye-candy action, a good-looking RPG with appealing characters. Japan-only right now.)Nanostray
(Very awesome shooter game, it's visually appealing and the frame rate is smooth too. ^^)Nanostray 2
New International Track & Field
New Super Mario Bros.
New Zealand Story DS
Ninja Gaiden: Dragon Sword
Ontamarama
Osu! Tatakae! Ouendan
Phantasy Star Zero
Picross DS
Pinky Street: Kira Kira Music Hour
Pinky Street: Kira Kira Music Night
Planet Puzzle League / Puzzle League DS / Panel De Pon DS
Pokémon Mystery Dungeon: Explorers of Darkness
Pokémon Mystery Dungeon: Explorers of Time
Pokémon Diamond
Pokémon Pearl
Pokémon Platinum
Pokémon Ranger
Pokémon Ranger: Shadows of Almia
Professor Layton and the Curious Village
Puchi Puchi Virus
Puyo Puyo Fever / Puyo Pop Fever
Puyo Puyo Fever 2 / Puyo Pop Fever
Puyo Puyo! 15th Anniversary
Rainbow Islands: Revolution
Resident Evil: Deadly Silence / Biohazard: Deadly Silence
(I kick everyone's behind at this game~ My best time is 48 minutes~)Retro Game Challenge / Game Center CX: Arino no Chousenjou
Rhapsody: A Musical Adventure
Rhythm De Cooking
Rhythm Tengoku Gold / Rhythm Heaven
(I 100%'d it. Great use of the Touch Pen. Addicting music. You will love it~)Rockman EXE 5 DS: Twin Leaders / Mega Man Battle Network 5: Double Team DS
Rockman ZX / Mega Man ZX
Rockman ZX Advent / Mega Man ZX Advent
Rune Factory: A Fantasy Harvest Moon
Rune Factory 2: A Fantasy Harvest Moon
Ryuusei no Rockman: Pegasus / Mega Man Star Force: Pegasus
Ryuusei no Rockman: Leo / Mega Man Star Force: Leo
Ryuusei no Rockman: Dragon / Mega Man Star Force: Dragon
Ryuusei no Rockman 2: Berserk X Shinobi / Mega Man Star Force 2: Zerker x Ninja
Ryuusei no Rockman 2: Berserk X Dinosaur / Mega Man Star Force 2: Zerker x Saurian
Ryuusei no Rockman 3: BLACK ACE / Mega Man Star Force 3: BLACK ACE
Ryuusei no Rockman 3: RED JOKER / Mega Man Star Force 3: RED JOKER
SBK: Snowboard Kids
(Just as good as the N64 games. Characters are normal-size now instead of SD Chibi)Scurge Hive
(A top-view Metroid clone)Shining Force Feather
Shin Lucky Star Moe Drill: Tabidachi
(Lots of fun game references and jokes, a lot of text though... Don't have to be a fan to enjoy it.)Sigma Harmonics
(Good-looking adventure game by Square Enix. Played by turning the DS side-ways. Japan-only...)SNK vs. Capcom: Card Fighters DS
Sonic Chronicles: The Dark Brotherhood
Sonic Rush
Sonic Rush Adventure
Soul Eater: Medusa no Inbou
Super Mario 64 DS
Super Monkey Ball: Touch & Roll
Space Invaders Extreme
(Square Enix worked on this. Very addictive. Boss battles and fun music beating added to the mix)Star Fox Command
Steal Princess: Touzoku Koujo
(A fun top-view adventure game. Not hard to understand at all)Suikoden Tierkreis
Summon Night: Twin Age
Super Princess Peach
(Seriously! How can you miss this? ;w;)Taiko no Tatsujin DS: Touch De Dokodon!
Tales of Hearts: Anime Movie Edition
Tales of Hearts: CG Movie Edition
Tales of Innocence
Tales of the Tempest
Teenage Mutant Ninja Turtles 3: Mutant Nightmare
(I know, it's not Classic Turtles, but still good. ^^)Tengen Toppa Gurren-Lagann
Tetris DS
The Legend of Spyro: Dawn of the Dragon
The Legend of Zelda: Phantom Hourglass
The Simpsons Game
The World Ends With You / Subarashiki Kono Sekai: It's A Wonderful World
Trauma Center: Under the Knife
Trauma Center: Under the Knife 2
Valkyrie Profile: Covenant of the Plume
Viewtiful Joe: Double Trouble! / Viewtiful Joe: Scratch!
Wario Ware Touched / Sawaru Made in Wario
Wario: Master of Disguise
Xenosaga I & II
(2D remake of the first two PS2 games. Japan only)Yatterman DS
Yatterman DS 2
(Fun platform game ^^)Yoshi's Island DS
Yoshi Touch & Go / Catch! Touch! Yoshi!
(It's like a "tech demo" testing the ability of the DS. It's still good. ^^)Yosumin. DS
Ys Strategy
... I wasn't even finished, guys.
