V good idea ! I won't include systems that I didn't get brand new, or recently after they had released.
From memory...
ZX81 - I just wanted a computer and was waaay to young to have the skillz needed to make a ZX80.
Spectrum - JSW. JSW JSW JSW. For cripe's sake it was the in thing back then. Including that really annoying color code thing. Apparently they invented a technology called 'lenslock' but it was so darn good that the M.O.D nicked it. However, thinking a bit harder it was actually Daley Thompsons, Jet Pak and Pssst (and Trans am likes). I had to share the speccy with my brother, so we had to mutually agree on games we both wanted it for so we could plan our attack and make mum get us one
I REAAAAALY wanted a C64 because of Impossible Mission. I used to go to a computer shop in Morden to get my Speccy games and listening to it go "Kill him my robots" and stuff just absolutely blew me away. But alas, we simply just couldnt afford a C64 because it was too soon after Dad died and we had to really pull in our belts. I never did own a C64.
C16 - got it on clearance from Currys for 30 quid because I wanted the fruit machine sim.
Vic 20 - hand me down from my cousin, but I really wanted it for the fruit machine sim.
NES - Mario. I cannot even tell you the hours I used to spend in Debenhams playing the display model. Also Rad racer (I sold my NES but got another one when Rad came out).
Master System - I just wanted Out Run and Shinobi. Oh and of course Hang On !
PC Engine - I played Vigilante round a mate's house and it was just incredible. I waited about three months for him to get an import MD before he finally cracked and sold it to me. I also loved Atomic Robokid. Fantastic little game. Of course bigger and better things came later (god the PAL booster was poo) but this thread's about what made you want the system
MD - believe it or not Altered Beast. I really liked it in the arcade. Oh, and I thought Rastan Saga was coming out on it (might have in the end) and seeing Thunderforce 4 on my pal's import system gave me a boner. He stayed over at my house for three days and we didn't sleep a sodding wink because of that game.
SNES - TBH at the time I knew little of Marioworld. I just saw it in Freemans and mum asked what I wanted for xmas/leaving school present so I said SNES. Fuggin glad I did now, Marioworld is one of my top ten games of ever.
Atari STFM - a mate of mine had summer olympiad on his (he had the old pooey ST that had a monitor but was soon ditched so fuck all worked on it) but I wanted one. For a LOOOONG damn time before I managed to scrimp up the 230 sheets from doing a paper round. Also Hostages. What an incredible game.
Amiga - First game I saw was Premiere and wanted one.
3DO - I got one quite late (for 130 quid new) because Fifa looked incredible. Oh and I saw a ep of Gamesmaster and saw Road Rash and fell in love.
32x - Virtua racing. Nuff said really.
Saturn - my cousin rented a saturn from BBV about a week after it came out. We spent about 4 days with no sleep playing Daytona. I was in love. head over heels... It took months to save up the 400 quid (first time Id ever paid that much for a console).
PSX - Worms. My cousin had a PSX (got it knocked off from somewhere) and he rented worms and me and him and two of his pals had the best laughs ever. God what a totally evil game.. Youd plot against one another, backstab and kiss your mate's ass trying to get him to attack someone else.. haha, pure gaming hilarity.
N64 - TBH I had no idea what was out on it because I got mine import about two days after it came out in Japan (mate flew over with some empty suitcases). I had Pilotwings with mine and had to play it in B&W because there was no RGB box at the time and no conversion. I played it like that for about two months before finally getting a RGB cable (with a box on). I just wanted one so bad because 'Ultra 64' made me piss my pants in excitement tbh. Oh, and I LOVED Cruisin USA in the arcades.
Cube - Again, it was just my mission to have the latest Nintendo. Right up til the cube the big N were my heroes.
Xbox - just because to be totally honest, it looked different.
PC back in the day - Stunt Island, Nascar and Indy car racing (486DX2 66 versions)
PC 2000 onward - NFSU, Doom 3 HL2 etc. All of which have made me spend stupid money on cutting edge hardware, only with Doom 3 the buzz lasted about three days. I never played it again.
If I've missed any I'll add em with an edit. I only got about 3 hours sleep last night so I'm a bit floaty and delirious lmao.
Edit.
Neo Geo - Baseball Stars 2.
Mega CD - Night trap because of all the crap it caused in the media. Mind you the 3do one sniped the CD's ugly ass version.
DC - because Sonic had a fishing bit in it (the fat cat thing).