1. Super Smash Bros. Brawl. The hype I had for this game, and the fun I've had with it, will never not be real. I still remember watching Sonic "come from far away at supersonic speed" repeatedly after he was announced.
2. Resident Evil.
Yep.
I got Resident Evil along with Super Mario Sunshine and PSO on the GameCube at the same time. Well, Sunshine was for me, PSO for my parents (they played Everquest) and Resident Evil for dad.
As a result of peeking at him playing it, this game haunted me in my nightmares and such for years before I played it when I was around 12.
And you know what? I never enjoyed a game more. I challenged my fears and ended up with a game whose aesthetic, characters, music and gameplay I have a never-ending respect and adoration for.
Sometimes I still have nightmares about it. Good nightmares.
3. The Legend of Zelda: The Wind Waker / Ocarina of Time.
I like Twilight Princess more, as a game but especially for a certain really great character, but I simply have a permanent emotional attachment to these games. The ending theme of OoT and it's version of Zelda's Lullaby quite literally, make me "cri evrytiem".
(Especially the new Staff Credits 2 in OoT3D, all these years and finally the Zelda theme is in OoT).
4. The Last of Us. Ellie.
5. Demon's Souls. Man, I just really, really love this game. It is just perfect.
6. Phantasy Star Online. Everything about this game makes me incredibly and purely happy, it's design, it's music, everything. I've never even played it online, either.
7. Super Mario 64 / Sunshine. I think everyone is at least a little sentimental for the former.
...
Note: Taking sentimental to mean general emotional attachment to.