I'm going to list the first game of each letter as they appear on my shelf.  You could use your profile collection, or whatever, but only list one game per letter.

Ape Escape 2

Baten Kaitos: Eternal Wings and the Lost Ocean

Cubivore: Survival of the Fittest

Donkey Kong Jungle Beat

Eternal Darkness: Sanity's Requiem

Final Fantasy: Crystal Chronicles

Ghosthunter

Haunting Ground

Ico

Jet Set Radio Future

Kirby Air Ride

Luigi's Mansion

Mario Golf: Toadstool Tour

NHL Hitz 20-02

Odama

Pac-Man VS.

(No Q.  Has anyone a Q?)

Resident Evil

Skies of Arcadia Legends

Tales of Symphonia

Unison

Vexx

Wario World

Xenosaga

Yoshi's Island DS

Zone of the Enders: The 2nd Runner 

No thanks, way to lazy.

hmm, this will be tough...

 I listed a game for each letter, but only if I've at least played a game with that letter. Most games on the list I own.

Aladdin
Banjo Kazooie
Contra
Donkey Kong Country
Eternal Darkness
Fire Emblem: Path of Radiance
Golden Eye 007
Hook
Indiana Jones
Klax
Legend Of Zelda: Ocorina of Time
Metriod Prime
NHL Hitz 2002
O (I've never played a game that starts with O)
Pikmen
Q-Bert
Resident Evil
Super Mario Galaxy
Tales Of Symphonia
Unreal Tournament
Vectorman
Wetrix
X-Men
Yoshis Cookie
Zoop