Basically a game that you were convinced could not be done on the old consoles or a game that came out earlier in the generation and really shifted your focus to the new generation or even just some graphics that made you think it's time to go get a new console.

For me it was Gears of War, for a long time (from about 2002 to 2006) I had pretty much not looked at the PSP, DS, PS3, 360 or Revolution at all, I used played the majority of the great PS2 games, but had mainly become a WoW player and thought I wouldn't buy a console again.

It wasn't until  the fall of 2006 that I started paying attention to the new consoles. The WoW guild I was in imploded and I quit the game (one of 4 times I've quit since). Right around that time, Microsoft's great Gears ad campaign was in full gear and I would see it constantly on tv and it was the first game on 360 that I really thought was very far ahead of other games geaphically which got my attention at first. After looking more into it, the over the shoulder shooting reminded me of RE 4 which was my favorite console game at the time and the cover system looked fresh and interesting to me.

That and Viva Pinata (yes I know polar opposites) looked 'next gen' like no other 360 game had before. Viva Pinata looked so colorful and clean and so bizarre that I really wanted to try it out despite the box being so embarassing to take to the cash register (some plastic toy looking thing). After a while I saved the money and went and got the orginal 360 (20 gb, 400 dollars) with Gears and Viva Pinata and never looked back after that.

Got myself an HD tv about 3 months later which made Gears look otherworldly (word?) at the time and started building up a 360 collection and I was a console gamer again :P

For me it was the marketing for Assassin's Creed. Irony was that the game turned out quite average once you get past the nice visuals (but poor framerate).

Which game convinced me to buy which console?

Their was no game that lead to me buying a next generation platform. I wanted a Wii because I was a major Nintendo fanboy. To me Nintendo could do no wrong and the idea of the Revolution in gaming had me far more interested than any game could. I loved my GameCube and obviously wanted the next console in Nintendo's line up.

While I never bought the Wii for a specific game I did buy my 360 and PS3 due to specific games!

Halo3 got me to buy a 360. Sure I had played Halo at friends houses and Halo2. But never did I buy an X-Box for them. However when I saw Halo3 I was in awe, I bought my 360 about a month before Halo3 launched. I've got to say Halo is definatly a platform seller I'm pretty sure their were plenty of other people who bought 360 just for Halo3.

FullAuto2:BattleLines/LittleBigPlanet got me to buy a PS3 this boxing day. I am a major anti Sony person of course I never actually bought the PSOne or PS2 (Both were at my foster home). However Little Big Planet and Full Auto 2: Battlines forced me to pick the platform up. I loved FullAuto on the 360 and just had to get my fix!

Was their ever a title that caught me in awe of the next generation?

Yes Halo3 for me kicked off the start of the next generation. Sure 360 had plenty of pretty games but nothing that screamed next generation. All in all I considered the 360 not much better then the X-Box up untill I saw the first Halo3 trailer!

..... so far ?

Baldur Gates
system shock1/2
Halif life2/ep1/2
Stalker/priboi story
Mount and Blade
L4D
Planescape Torment
Persona4
GoD of War 1/2
Shadow of the colosseus

More seriously, what will make me FINALLY buy a PS3 ?

==> The Last Guardian (guaranted)
==> GT5 (perhaps)
==> GoW3 (they will need something better than what they have shown at E3)
==> MGS4 (!)

well i never went anywhere since i'm a sony fanboy (and happy to be one)
But i opened up to the xbox 360 due to the Halo franchise.
I nearly bought a 360 but MGS4 preserved my loyalty to sony xD
I still hate the Wii though even though i supported its past consoles
Gamecube , NES , N64...
No offence xD

Yes, it was a very average game, but it did look pretty, hopefully this new one is better.

The wiimote and its gameplay possibilities were the reasons I got a Wii.
Uncharted franchise and Heavy Rain where the reasons I got a PS3.
Both screamed "next console generation" to me.

Assassin's Creed dragged me into this generation from the last. Very keen to get Assassin's Creed 2, now. The game to get me to upgrade my PC to the current gen's specs was Warhammer Online. Amusingly, I didn't play it that much, but have played games like Gears, Fallout 3, Mass Effect, Empire: Total War, and the like since, which has made it worth every penny.

I also got to play the PC version at one of my friends. We had a look at it for around 15 minutes and obviously it looked and played awesome. Thing is, it gets repetitive real quickly.

from what I have read, this one will be largely better.
I m expecting tonne of threads about it in the near future.