Intellivision - no idea, my dad bought all the sports games along with the system, so it had to be one of those
NES - SMB, blew my mind first time I played it at a friends. Spent the next several months begging my parents for one, only to be told I had to earn money for it myself. Not easy when you're in elementary school and don't get an allowance, let me tell you!
SMS - I think I put in Ghost House first, since that was one of the games I got along with the system for Christmas, and the card format was so different I had to try it.
Genesis - Altered Beast, the pack in. Loved having "the arcade" at home (even if in retrospect it wasn't "the arcade", and a very limited, short game)
SegaCD - Don't recall, but had to be one of the numerous pack ins. Doubt it was that Sherlock Holmes garbage, so either Sol Feace or one of the disappointing 4-in-1 ports
32x - I think I rented Knuckes Chaotix first.
TG16 - Keith Courage, pack in, meh.
TGCD - Y's 3. Yeah, I got that before Y's 1&2 because 3 was all that store had!
Saturn - Virtual Fighter, pack in pack in pack in. Very quickly rented Panzer Dragoon and Clockwork Knight, then bought them.
PSX - Hey, where's the pack in? Don't recall if I played Tobal No. 1 or Power Move Pro Wrestling first, since they were the first games I bought.
N64 - It's a me, Mario! Not a hard choice when the only other game out was Pilotwings. Not that Mario is ever a hard choice.
Dreamcast - Resident Evil Code Veronica. Actually bought the system just because I really had an itch to play that. Not that I didn't want the system eventually anyway, but I was just really in the mood for that game when I broke down and bought one.
PS2 - Resident Evil Code Veronica X. Owned the game for 6 months before I owned the system, lol
Xbox - Should have been Silent Hill 2. Got the system for Christmas, along with SH2... the PS2 version... Had to go out the 26th to exchange it. First thing I popped in was an OXBM demo disc, remember playing a demo of one of those Abe's [whatever] games first. First actual full game... I rented Halo and DOA at Hollywood Video (since they were open Christmas (and still in business)) think I put Halo in first. Neither game thrilled me.
Gamecube - rental of Luigi's Mansion. First game I actually bought was Resident Evil.
360 - Kung Fu Panda. HEY A PACK IN! I REMEMBER THOSE!!!!! Got to the end of a level and the system crashed, with 3 red lights (OH NOES!) fortunately it was a false alarm, system is still running to this day, just over 5 years later. Never put KFP back in the system, though. Spent the rest of the night with Lego Indiana Jones, then got Fallout 3 the next day, that kept me busy for a long time.
Wii - New Super Mario Wii.
PS3 - Got it for Christmas, didn't get any games... So had to make due with trying my PSX games of all things (since PS2 BC was long gone by that time, I got a slim). No idea what the first one I tried was. Day or two later got used games from GameStop (THE HORROR) in a B2G1 sale. Think 3D Dot Game Heroes was the first I tried. The other two were God of War Collection and God of War 3.