In terms of impact only two games have delivered this for me; Metroid Prime and Uncharted 2: Among Thieves. For both I didn't expect so much emmersive content and unexpected length. Both outdo their sequels in that respect, while Uncharted 3: Drake's Deception is one of the most enjoyable games I've played but the impact just was not there. The other Metroid Prime's overall lacked in more than just impact. I'm sincerly hoping I can replicate this again, but I only think this will occur if I introduce myself to a new franchise. 

Oh I've experienced a few games like these, Vice City, SSX3, Resident Evil, COD4, Uncharted 2, BFBC2 to name a few, there are plenty more.

They easily had an impact on me as I played most of them with little to no knowledge about them or even about the industry at all (2009 and before). But I can no longer play video games in a vacuum as I'm so in tune with the industry nowadays so I always know what's going on and what I'll enjoy sometimes a year before it comes out, so these kind of games are becoming very rare for me.

This generation it was Metal Gear Solid 4, Call of Duty 4, Final Fantasy XIII and Tales of Vesperia. All of those games blew me away and showed me something I had never seen before.

Modern Warfare 2, Uncharted 2: Among Thieves and Assassin's Creed 2 came close to blowing me away. As much as I want this generation to last, it has gone stale to be honest, I don't think I'll be blown away by games like that this generation or possibly ever, I'm too into gaming, it was far more enjoyable when I was a "casual".

Some games have impacted me greatly, some final fantasies and zeldas and of course chrono trigger.

Vice City, Kingdom Hearts 1, and Metal Gear Solid 3.

Recently RDR and Bioshock.

Hmm... Metroid Prime 2 way way more enjoyable than 1 imo. One of very few games with such a long story mode that I actually fully replayed and enjoyed throughout. I guess the awesome multiplayer played a big part as well though ;)

OT: The greatest impact in gaming for me would be my first Halo:CE play-through. It's amazing atmosphere, exploration moments and fluid shooting action has never been replicated, again imo.

It will come as technology matures. Your first true unscripted conversation with an NPC will feel like magic. And we still have mind control, eye control, and emotion control to look forward to. Not to forget advances in 3D display technology.
On a more short term note, procedural gameplay, evolving narrative, advances in radiant AI. Hopefully next gen has enough memory and cpu power to provide these new experiences.

This year still had it's impact on me with Terraria, Pixeljunk sidescroller (that last level is amazing) and Dark souls. And the amazing HD version of Ico and SotC.

The CD-i Zelda games.

This gen?
The original Mario Galaxy and The Legend of Zelda: Twilight Princess.

Overall: I guess Chrono Trigger.

The first games where I first thought 'omfg I didn't know a game could be this cool' were FFX and MGS3, and nothing has come since that has given me that feeling. But then again I was a teenager back then and today I would probably have gotten less of an impact from them.