I've never bought a console for just one game. However, there have been certain games that tipped my hand from "I'll pick this up someday" to "I'll go get this now."
NES: Parents bought it for one of my birthdays. It was the pack that came with a second controller, Zapper, and the SMB/Duck Hunt cart. Now that's a system bundle!!
Genesis: For some reason, my sister and I were really into beat-em-ups, so we had to get this for Streets of Rage 2 and Golden Axe 2. However, we also liked Sonic.
SNES: Chrono Trigger. I was a late adopter to the SNES because the Genesis was satisfying enough to me for a long time. But Chrono Trigger was just too good to pass up. I subsequently went back and picked up Final Fantasy 3 (well, VI) and Earthbound.
N64: Foolishly assuming this would continue the legacy of the SNES, I picked one up the summer of '97 when Star Fox 64 came out. I still have that insane video that Nintendo sent out to advertise the game, and I recall having to paint the shed at our old house to get the console and Star Fox 64.
Playstation: An inability to find Ocarina of Time in the winter of '98, along with a horrible famine of RPGs on the N64, led me to finally break down and buy a PS1. The game I bought it for was Xenogears, weirdly enough, though I did pick up a ton of games alongside it.
Dreamcast: Shen Mue. Quite simply, that game looked and was the most advanced and amazing thing I'd ever seen. This was the one time I blindly bought a console without knowing what else I wanted for it. Thankfully it had a pretty decent library then and afterward.
PS2: This is going to sound stupid, but Baldur's Gate: Dark Alliance. I was and am a huge Diablo fan, so this game was up my alley. I bought it before I even had a PS2, even. Yet there was also Final Fantasy X, which my friend got for Christmas and all I did one night was watch him play it for 6 hours straight.
GBA: Castlevania: Circle of the Moon. I was and am a huge Symphony of the Night whore, so the idea they were doing a spiritual successor to it made me buy a GBA soon after launch. Super Mario Advance 1 was also really damn good, though.
Gamecube: My parents got me this for Christmas along with Rogue Squadron II, Pikmin, and Smash Brothers Melee. People make fun of all Nintendo consoles for having a weak launch and software library in its first few months, but Gamecube was different. Pikmin and Smash Brothers came out a few weeks after the launch but before Christmas, so there were at least three games you had to have for Gamecube by the end of 2001.
Xbox: A combination of Fable and Halo 2 put me over the edge. Sure, there was KOTOR 1 and a handful of other good-to-great titles, but Fable and Halo 2 were crucial to the Xbox entering my household.
DS: I wasn't completely sold on the DS until I played New Super Mario Bros. and realized that it wasn't just going to be niche stuff and gimmicky non-games like Nintendogs. So I came full circle from my parents getting me a NES with Super Mario Bros. to getting a DS (Lite) for New Super Mario Bros.
