The system sellers that got me in this generation were many so I'll only list a few on each system that I own.

DS The games that I just had to play were

Mario Kart DS 

Castlevania Dawn of Sorrow

Final Fantasy III remake

New Super Mario bros

Seriously the DS might just be Nintendo's best system ever.

Wii Some of the best Nintendo first party games were made for Wii The ones that made me buy it were

Super Smash Bros Brawl

Mario Kart Wii

Metroid Prime 3

Super Mario Galaxy

PS3 some of the games I knew at the time I'd need the system for were

Final Fantasy XIII

God of War III

Metal Gear Solid 4

Really all things considered the PS3 has some of the most awesome 3rdparty support this generation imo.

PSP I instantly knew I'd be buying the PSP this gen when I found out early on that there was a Metal Gear game and that Medievil was being remade the other games that caught my interest were

Mega Man Powered Up

Crisis Core Final Fantasy VII

Grand Theft Auto Liberty City Stories

The PSP really does have a solid lineup.

PC really is an awesome platform for games. The ones that made me update my video card this gen were

Crysis

Mass Effect

Gears of War

I know the PC transcends generations but I thought it deserves a mention.

I'll also mention the Xbox 360 even though I don't have my own yet do to financial reasons. I have played my friends 360s and just some the games that I'd buy it for are

Halo 3

Halo Reach

Forza Motorsport 3

Alan Wake

Lost Odyssey

The Last Remnant

I really can't wait until I complete my collection of consoles this generation. 

Alright so what was/were the games that got you into this generation for each specific system you own?  

PC, because I will get this no matter what. It's a hobby to upgrade and build, and over clock.
Though Dead Space is my favorite on PC. I'd have to say Crysis because it looks so damn gorgeous.

PS3. MGS4, FFXIII

Xbox... um, my brother wanted to get it, because my PC couldn't play oblivion at that time. (Though I have it now  on pC :)

PSP: FF7 CC

DS: The world ends with you.

WII: my mom won a free one (I wouldn't have boughten it). but I'm looking forward to xenoblade and would have bought one for that Last story and The new zelda (I bought TP for gamecube)

360: Xbox live, friends, next gen console,

ps3 if i had one, for the amazing Little Big Planet

Wii:  no game in particular, just for the experience

PS3: when the price came down it was Valkyria Chronicles and Uncharted (still my favorite two games!)

360: Gears of War, Halo 3

I bought my 360 because it had early exclusives.

My Ps3 cause blu-ray and God of War 3 although I had my ps3 years before it came out.

Wii because everyone wanted it.

What were the games for the 360 that contributed to your decision to purchase one?

Wii: Wii Sports, Twilight Princess, promise of Brawl

DS: Super Mario 64 DS, Mario Kart DS

360: DDR Universe 2....

The Online gaming makes this gen for me!!!

PS3 my first system: Uncharted rocks the most, Infamous and littlebig planet.

360 its all about mass effect 1 and 2 as well as the gears original.

Wii has been fun for mariokart.

DS (2005):  No game in particular.  It just looked cool.  (First game was "Feel the Magic")

360 (2007):  Unable to find a PS3 and I wasn't going home empty handed. (First game was "Kameo")

Wii (2007):  No game in particular.  Saw one in store and couldn't believe it.  (First game was "Resident Evil: Wii Edition")

PS3 (2008):  Metal Gear Solid 4

PSP (2009):  Wanted to watch movies while I "worked" at my new job.  (First game was "Rainbow 6: Vegas"). 

No game has been a system seller for me since PS1/N64

I got a PS1 for Spyro and an N64 for Super Mario 64 (ironically, I never got SM64, but got the N64 because I thought the game was awesome)

I wanted a Dreamcast just because it was the new thing, but I didn't get it until like 2001 when it got liquidated and was $50 (which I bought in $1s from saving allowance).

I got a PS2 because the PS1 was just so awesome, and all my friends had PS2

I got a PS3 because this is the first generation where I'm in total control of my game purchases and research. With the PS3, I strongly followed the "just wait" motif, and bought it at $400 knowing that all the great Sony IPs would come to it, along with 3rd party games like GTA4 and MGS4

I got a 360 because it just so dominating in the US, and all my friends had one and were playing CoD4 and Halo, so I just bought one. It was also, however, an impulse buy because someone I worked for had sent me a check for $200 for doing little work for him (he overpaid, by ALOT), so along with some game trades, the 360 cost me, out of my own personal pocket, like $15