I've been around this blue marble for awhile, so for the most part, my firsts tended to be either the pack in that came with the system or a release title. No particular order to my list, but systems are grouped by company. The ones with a * are systems that I did not personally own. The ones with ~ are systems that I still possess.
Atari - Pac Man
Atari Jaguar - Raiden*
NES - Super Mario Bros
GB - Tetris
SNES - Super Mario World~
N64 - Super Mario 64
Virtual Boy - Teleroboxer*
GBC - Tetris DX
GBA - Castlevania: Cirlce of the Moon
GC - Star Wars Rogue Squadron II: Rogue Leader
DS - Spiderman 2~
3DS - Rayman 3D~
Wii - Wii Sports
WiiU - Mass Effect 3*
Sega Master System - Shinobi*
GEN - Altered Beast
GG - Columns
32X - Knuckles Chaotix*
SCD - Sewer Shark
SAT - Panzer Dragoon
DC - Sonic Adventure
PS1 - Battle Arena Toshinden~
PS2 - SSX~
PS3 - Untold Legends: Dark Kingdom~
PSP - Lumines~
PSV - Rayman Origins~
XBX - Halo
360 - Call of Duty II
Neo Geo AES- Fatal Fury~
Neo Geo Pocket Color - Biomotor Unitron
Turbo Grafx 16 - R-Type
Turbo CD - Rondo of Blood
PC - Doom~
3DO - Super Street Fighter II Turbo (Yes, I owned this garbage system. Got it at a flea market for 30 bucks with games.)