RPG/STRATEGY:
-Golden Sun DD ( also a big jrpg fan and i liked Golden sun: Dark dawn.)
-Suikoden tierkreis
-Final Fantasy 4
-Front Mission
-FF CC: Rings of fate
-Pokemon B & W
-Advanced wars

FPS:
-C.O.R.E
-Moon
-Dementium 1 and 2
-Metroid Prime

RACING:
-Sideswiped
-Tony Hawks Downhill Jam
-Donkey Kong Racing

SPORTS:
-Top Spin 3
-Skate it
-Track & Field

PLATAFORMERS:
-Mario 64 DS
-New super Mario bros.
-Sonic colours

VISUAL NOVEL:
-Hotel Dusk
-Last window
-Time hollow

ACTION ADVENTURE:
-Castelvania series
-Ninja gaiden
-Zelda
-Resident evil DS

Hmm, lets see..

if you dont have a Wii for Wiiware, try Phoenix Wright: Ace Attorney on the DS

also, Advance Wars DS and Advance Wars Days of Ruin (By far my favorite DS game ever, and one of top 25 games ever)

Sonic Rush was amazing. These have been my best experinces with the DS

F0X said: The World Ends With You Castlevania: Dawn of Sorrow Okamiden Advance Wars: Days of Ruin Mario and Luigi: Bowser's Inside Story And just because it has a special place in my heart... Phoenix Wright: Ace Attorney

Add Castlevania: Order of Ecclesia and Final Fantasy Tactics A2 to this list

and Shin Megami Tensei Devil Survivor if you can find a copy

You seem to like SRPG so I recommed you Shin Megami Tensei: Devil Survivor and Shin Megami Tensei: Devil Survivor 2 both are great games, the first one got a port with extra content on 3DS so you may want to buy that one instead of the DS version. The World Ends With You and Castlevania: Order of Ecclesia are superb games too.

Hmmmmm tonnes of great DS games out there.........

Heres some of my personal faves (they have all pretty much been covered, but oh well)

Sonic Rush
Castlevania: Portrait of Ruin
New Super Mario Bros
Ninja Giaden: Dragon Sword
Sonic Colours
Castlevania: Order of Eccelsia
Tony Hawks American Sk8land (best TH game on DS)
Resident Evil: Deadly Silence (Rebirth mode breeds new life in to this classic game)
Castlevania: Dawn of Sorrow (ain't completed it yet because the copy i bought was German, hope to get an English copy soon)
Grand Theft Auto: Chinatown Wars
Mario Kart (although it was a bit too short for my liking)

you will get all of these cheap as chips these days shopping around (although the Castlevania games seem to maintain a 15-20 pound price tag)

Etrian oddysey if you like dungeon crawlers
Hotel dusk,999 and the phoenix series for story based games.
Monster tales, kirby, contra, sonic rush/colors for platformer.
Advance wars, ff tactics A2, in the srpg department
DQ series, pokemon, shin megamis series, mario&luigi rpgs.
Proffesor layton and henry hatsworth for puzzles.
rythm heaven and elite angels for rythm games.
KH days, world ends with you, castlevania games,mario kart,

That would cover the basics for me.

IMO the DS has the best lineup of any platform IMO, especially as your tastes are very similar to mine (JRPGs and Platformers). IMO the top 5 DS games are as follows (I'm excluding Mario Kart as I think you should get 7):

The World Ends With You
Dragon Quest V
Pokemon Black/White
Pokemon Heart Gold/Soul Silver
Advance Wars: Dark Conflict (known as Days of Ruin in the US)

Pokemon Diamond & Pearl
Pokemon Heartgold & Soul Silver
Pokemon Black & White
Pokemon Black 2 & White 2 [Comming this fall]
Mario Kart

The only reason to own a 3ds or a ds is pokemon

I don't think that it was a port. I know there are other mana games though.

C.O.P is a sandbox with amazing graphics