World Series got me to go buy a Genesis and Blue Stinger convinced me to buy a Dreamcast after playing the import version.

I usually buy all new consoles by MS Sony and Nintendo. as far as hand helds go I will buy the DS for Mario and Zelda games coming out. I bought the PSP for no game in specific and sold it a while later due to lack of games. I bought the GBA for the Zelda games

No console has had a single game that said BUY ME to me, until recently. The Zelda: Phantom Hourglass trailer sold me on getting a DS whenever the Lite hits. The New Mario videos seem to have cemented the purchase.

NES: SMB
SNES: SMW
Genesis/32X: Star Wars Arcade
N64: Super Mario 64
PSX: FFVII
GBC: Link's Awakening DX, impending trip to Europe where I wanted something to do on the flight(s)
PS2: Madden 2001
DC: It was cheap
GBA: Just liked the new hardware
GC: Star Wars: Rogue Squadron
XBox: Halo

DS: Haven't been impressed enough yet to want one, but with the DS Lite, and the new Zelda and Mario games, I'll have one by the time Zelda comes out

2600 - The Empire Strikes Back (Without having played the game, mind you-- I was just so excited about a Star Wars home game that I went NUTS for this.)
NES - The Legend of Zelda (Octoroks, Tectites, and Leevers, too!).
PS1 - FF VII, with the added bonus of Gran Turismo.
DC - Jet Grind Radio was my first game, but the potential of cheap (copyable) games was the real reason.
GBA - Zelda: Oracle of Seasons, since I'd never had a GB before.
PC - I upgraded a few years back in anticipation of Star Wars Galaxies. Heh.
PS2 - Gran Turismo 3, and the potential of FFX and Kingdom Hearts.

DSLite - I will buy this ASAP for Advance Wars DS and New SMB, whenever they hit the US.

Hmm,
NES:Not one game specifically, my brother and I just wanted one so my mom bought it for is at the end of the school year.
Genesis:NHL Hockey made my brother and I put it on our Christmas wish lists
SNES:Zelda
PS1: NHL 98
PS2: Metal Gear Solid 2 and Gran Turismo 3
Cube: Resident Evil and Rogue Leader
XBox: Halo
360: No specific game really, PD Zero was the first game I bought but it wasn't really a system seller to me. The thing that really got me to buy one was that I'd already sold my XBox and wanted to play Halo and Halo 2 again so I opted to just get the 360 when i could find one

I also suggest picking up Mario & Luigi Partners in Time. I just bought a DS for the same reasons you're planning on it, and scooped up this title and absolutely LOVE it.

Atari 2600 - Kaboom!
NES - Kung Fu
Master System - Hang-On
Genesis - Ghouls'N Ghosts
SNES - Super Mario World
Nintendo 64 - Super Mario 64
Gamecube - Super Smash Bros. Melee

Some systems I've just bought (or had thrust upon me) without there being a particular game, but these are the system that had that one game that convinced me to buy.

NES: Super Mario Bros.
The first time I saw this, it was like my dreams had come true. I had to have an NES...bad!! I think I discovered it around June of 1988. My birthday was in May, and Christmas was months away, but I took every oppertunity I could get to remind everyone I saw that I wanted a NES. It paid off too, because around September, my grandpa took me to Wal*Mart and let me buy the NES with SMB & Duck Hunt. That was the moment when I became a gamer.

SNES: Super Mario World & Top Gear
Those were the two games my best buddy had on his SNES, and we played those games a lot. I didn't even like racing games and I still don't, but we played it anyway, and loved it. I had a Genesis at the time, but eventually I managed to get an SNES to go with it.

N64: Super Mario 64
In the early 90's, I got into a PC gaming pretty heavy and all but gave up on consoles. By '96 however, my PC wasn't quite up to gaming specs anymore and my parents refused to buy me another one. They did, however, agree to buy me a gaming console for Christmas. I was in Toys R Us in Novemeber, and they had two kiosks running side by side; one with a PS1 running Crash Bandicoot and one with an N64 running Super Mario 64. I went to Crash first, and that kept me entertained for about 5 minutes. Then I went to the N64, and Mario 64 blew my f'ing mind! I was on the N64 bandwagon after that...

PSOne: Final Fantasy VII
...but I was eventually swayed into getting a PS1 as well by Final Fantasy VII. The first hour of this game really hooked me. Here we have this band of terrorists and we're carrying out this attack on the power station of this huge city in this smoggy Blade Runnerish future...it caught me off-guard. And although they're not that great now, I was mesmerized by FMV. It was an amazing experience for me at the time.

PS2: Silent Hill 2
While everyone else was Oooohing and Ahhhhing over Metal Gear Solid 2 footage, Silent Hill 2 was the only Konami game that concerned me. The original was one of my favorite games for the PS1 and one of the few non-RPGs I kept in my collection after moving to the next generation. I wasn't let down either, SH2 topped the original for me.

XBox: Project Ego
I prefer to believe that Project Ego was silently cancelled at some point in it's development cycle, and that Fable is a totally different game that they made to take it's place. It helps me sleep better.

NES - Castlevania
Genesis - no game in particular, but the console itself was free
SNES - Mario Kart
32X - Doom
Playstation - Ridge Racer, bought with system at launch
Saturn - Sega Rally & Daytona
N64 - Mario Kart 64
Dreamcast - San Francisco Rush 2049
PS2 - Gran Turismo 3 & GTA III
XBox - Halo & Splinter Cell
Gamecube - Eternal Darkness

Vision Gran Turismo has already sold me on the PS3

NES: Metroid
SNES: Super Mario World
Sega Genesis: Mortal Kombat
Nintendo 64: Goldeneye
Dreamcast: NBA 2K
Playstation 1: Resident Evil 2 and Metal Gear Solid
Playstation 2: GTA 3
Xbox: Halo/Splinter Cell
GBA: Super Mario World and Castlevania
Gamecube: Metroid Prime

New Super Mario Brothers --> DS Lite
Starfox 64, Super Mario 64 --> Nintendo 64
Sonic --> Game Gear
Super Mario World --> Super Famicom
no game interested me but I found one available when it was still rare --> 360
Final Fantasy 1&2 --> GBM
Taiko DrumMaster --> PS2 again (after I gave mine to my cousin)
Crazy Taxi --> Dreamcast
cause it's SONY --> PSP

PS1: Tekken 3 and FFVII
X-Box: Chronicles of Riddick & I always wanted to play Jet Set Radio Future
Gamecube: Mario Sunshine

& soon

DS: The newest Super Mario Bros and Brain Age

The other systems I got because it was they were the new toys on the market and seemed cool.

NEC Turbo Grafx-16 - I didn't really intend on buying this and my knowledge of gaming was rather limited at the time, but in the Xmas of '89 (I think, might've been later, not sure) my dad surprised me and my older brother with it. Keith Courage in Alpha Zone (the pack-in game) was pretty kickass though. So were the Bonk games and later Bomberman and Military Madness.

Saturn - Got it for Xmas when they had that three game pack-in (VF 2, VC and Daytona). But really it was so I could buy and play a home edition of Sega Rally.

PlayStation - Final Fantasy VII, back then I was pretty unfamiliar with what exactly an RPG was having grown up with a Turbo Grafx-16 and its library of mostly Zelda-ish action rpg's. This game looked so fucking cool though (saw it first on that stupid Gamepro TV show on what used to be Fox Sports New England or whatever and in EGM) that I cashed in the loose change that I kept in a jar and bought a PS1 around when the game dropped. Funny though I had to wait until Xmas to get the actual game as I had no money left over.

Dreamcast - This was something that also sort of just happened, as my brother, who was living outside of D.C. at the time while he was in college, found one of those early .com startups (whatshotnow.com I think) that had one of those click-enough-times-per-day-and-get-item-at-a-discount deals. We ended up getting it for $99 the Xmas after 9-9-99. Eventually it helped me realize the awesomeness that was JGR, Crazy Taxi, Soul Calibur, and Sega Rally 2. Oh yea, Virtua Tennis and the NBA 2k series too.

PlayStation 2 - This system was all about the sequels. Bought it for Gran Turismo 3, MGS 2, future FF's and GTA III.

GBA SP - Final Fantasy Tactics. I bought the system and game the day the game came out.

XBox - The minute I found out that Sega had signed an exclusive agreement to publish seven (or was it six?) games on Microsoft's system and that Panzer Dragoon Orta was to be one of the games I knew I had to have one.

Gamecube - The last system I bought. Got it because a coworker no longer wanted it, the fact it came with Zelda: The Wind Waker sealed the deal.

Lynx - Gauntlet - I swear nearly every launch lynx title was awesome.

Megadrive - Altered Beast - Hey it was cool at the time...

PS1 - Final Fantasy VII - I actually first completed this on a friends ps1, but it was enough for me to want my own ps1.

Dreamcast - Dead or Alive 2 (with other sega titles in the pipeline) - This game looked so good at the time. Had a lot of fun playing with friends.

PS2 - Silent Hill 2 - Best of the series!

Xbox - Halo

Gamecube - Mariokart DD - Urrghhh.... what a horrible disappointment. At least Tales of Symphonia was good.

DS - Nintendogs and GBA support

PS2: The .hack series.

After playing Halo for the first time over at a friend's place, I knew I had to get an Xbox.

Haven't bought another console since.

NES: Super Mario Bros-Duck Hunt
SNES: Super Mario World, Street Fighter II
N64: Mario 64, Goldeneye
PS1: Final Fantasy VII
Gamecube: Star Wars Rogue Leader
PS2: Grand Theft Auto III
GBA: Mario Kart Super Circuit
XBox: NBA 2K series
DS: best system/games since the SNES
PSP: Ridge Racer, UMD movies
Wii: controller alone

Gamecube: Resident Evil 4
X-Box: Doom 3

Every other system I have I bought because I wanted them. These are the only 2 systems that I had no previous interest in owning until said games were released for them.

Gamecube: Super Smash Brothers

playstation 1 Resident Evil. I remember buying a scratched up used version in the mid-1990`s because all the new vesions of it were sold out.

All of my other consoles I bought just 'cause, but I bought a PS2 for Grand Theft Auto 3.

I usually just buy a system because I want it. But after playing HALO on the XBOX, I went out and bought one.

The rest I just bought because I wanted them....not for one game in particular.

Systems I bought on my own, and the reason/games I bought with it...

N64: Super Mario 64
PSX: Resident Evil, MGS, Final Fantasy VII
GBA: Zelda: Link To A Past, any SMB port.
PS2: Metal Gear Solid 2, GTA 3
DC: Shenmue!
GC: Paper Mario 2
XBox: Star Wars: KOTOR
XB360: More on the system, then any games so far.

Vaguely in the order I bought them (I had an Atari 2600, NES and a SNES as a kid):

PS1 - self-present on my b-day. For FFVII, Chrono Cross (which I ended up not a big fan of), Tekken 3.

PS2 - sold PS1 and chipped in 50/50 with my g/f (now wife). She bullied me into it. Mainly as it was a PS1/DVD player combo with future Squaresoft support. Tekken Tag Tourney was the only PS2 game I had for over a year. I played more Dragon Warrior 7 on it than PS2 games (exempting Tekken).

Gamecube: Wife bought it 6-8 months after launch, so not my purchase. All about the Super Monkey Ball/Smash Brothers for me.

Dreamcast: Soul Calibur, Skies of Arcadia

NES - garage sale - mainly to play my old beloved cartridge of Dragon Warrior IV. And Mario. Gotta love da Mario.

Genesis - same garage sale. To play Shining Force 1/2 (DC emulation sound sucks). Golden Axe. Streets of Rage. Sonic too.

Sega Saturn : wife got it for me for my b-day. Mainly to play Panzer Dragoon Saga, D&D collection, and Street Fighter games. Never did get my hands on PDS or D&D collection import though, so it doesn't see much use.

Xbox: January last year. Street Fighter Anniversary with online play was the key factor, combined with Panzer Dragoon Orta, KOTOR, and wanting to know what the fuss was with this Halo game. None of which I've really played that much so far.

PS1: Wife wanted a FF7 strat guide. Buying a PS1 with some games and the strat guide was almost cheaper ($25 shipped) than buying the guide at B&N.