I didn't buy my first Atari 2600, but I convinced my parents to get one, believe it or not, because of Donkey Kong and Combat. My brother and I had a total frickin' blast playing those games way back when.
Back when I worked at Montomery Ward (late teens), I fell in love with Alien Crush for the TG-16. Bought the system just for that game. Of course, loved most everything else that came out for it since.
Wanted the Amiga even before it was released, but bought an A1000 soon after I had seen the incredible NewTek demo. Umm, like made the purchasing decision the same day I saw that demo in fact. lmao
Bought the SNES for Mario IV. Loved soooo many other games since then. Castlevania, Contra, Final Fantasy, Chronotrigger, Side Pocket, etc.
Bought the Jaguar for all of its promising game titles, which were really starting to suck before Tempest and AvP came out.
Bought the Gamecube because of Rogue Squadron. Liked only a few after that. Mario Kart I guess and I really can't remember too many of the others. Gottlieb pinball collection too.
Bought an XBox for the new Panzer Dragoon game, but can't remember too many others I thought were worth a damn besides maybe a driving game or too. I played a lot of Panzer Dragoon, I know that. By the time XBox, Gamecube & Dreamcast came out, my video game interests were starting to wane big time.
Bought an N64 for Mario64. Loved Mario Kart64, Shadows of the Empire, Rush 2049, Cruisin' USA and a few others.
Bought a Wii for its bundle of freebies (and then soon got rid of the thing). I did like the Star Trek military strategy game and Mario Kart of course. Had the 2-3 pinball collections for it and I can't remember what all else. This system and its cartoony look and floaty cursor feel got old real quick with me.
Bought a PS1 back in the day for Battle Arena Toshinden that featured Sophie, yay! Return Fire was fun as was Destruction Derby. I know I bought a handful of other games for it, but can't think of 'em right now. Nothing too memorable obviously. lol
Bought a PS2 recently for Guitar Hero. I have a bunch of games for it now, but would never have pursued anything else without the GH series. I have a HD in my system and most all of my games fit on 120GB. If I didn't have the HD, I'd probably tolerate the system even less as I hate load times and CD based gaming in general.
Bought the original Gameboy for Tetris. Pretty much hated every other game for it after that. lol
Bought the Saturn for Daytona USA and the promise of all the other great games for it like Duke Nukem 3D, Bomberman and more online stuff.
Bought an original NES back in the day for Mario Bros./Duck Hunt and the cool robot toy thing. Super Mario 2 and 3 rocked as well as only a few others though. Contra of course. Zelda, Pinbot. Didn't care for that many more games though, hate to say.
Bought a Commodore 64 back in the day for Pinball Construction Set and Sammy Lightfoot.
Bought a Sega Master System for Parlour Games and some of the cool RPG's for it at the time. Y's, etc.
Bought a 32X for its promise and Virtua Racing. haha
Don't remember why I bought an Atari Lynx to be honest. Didn't care for most of the games or its washed out blurry screen. I did think it would be nice to game on the go, but I never cottoned to portable gaming. Wait, I do remember thoroughly enjoying Rampart on the Lynx

Wanted to love Elvira's Pinball - but talk about blur city!
I did purchase a new TurboExpress though from TZD back in the mid 90's, only because it could play my awesome TG-16 library. But, alas... never got much use and I was too anal about my gaming to want to take my HuCards, let alone that system, out and about. Screen is waaaaaay too damn small too, even though the contrast and clarity is vastly superior to the Lynx.