First games:
Atari - Pong, Jungle Hunt and Tennis
NES variant (Micro Genius) - Legend of Kage (Kage is pronounced Ka-Ge and not 'Cage') and Battle Tanks
Sega Megadrive - Insector X and Midnight Resistance
SNES - Yuyu Hakushu and Secret of Mana
Neo Geo - Art of Fighting 2
PSX - Beyond the Beyond
I've since switched to handheld games.
Well along the years, a couple of games I remember more fondly are
Castlevania 2 (NES)
Bomberman (NES)
Double Dragon 3: The Rosetta Stone (NES)
Chrono Trigger (SNES)
Romancing Saga series (SNES)
Bahamut Lagoon (SNES)
Secret of Mana (SNES)
Front Mission (SNES)
Zelda: A Link to the Past (SNES)
Lufia (SNES)
Streets of Rage aka Bare Knuckles [I, II and III] (MD)
Herzog Zwei (MD)
Golden Axe 3 (MD)
Wani Wani World (MD)
Thunder Force IV (MD)
Vapor Trail (SNES)
Langrisser 2 (SNES)
三国志英杰传 (SNES)
Super Robot War G (PSX)
Tobal No.1 (PSX)
Tales of Destiny (PSX)
Star Ocean: The Second Story (PSX)
As you can see I'm quite a RPG junkie but the games I enjoyed most are actually the ones I played co-op/vs with my cousins and classmates. Playing console alone is half the fun only.
Thunderforce VI is a fantastic side-scroll shooter, beats gradius, parodius, r-type hands down.
Oh, how could I forget about Langrisser & Super Robot Wars..
played Romancing Saga? then ya quite a hard core gamer too!!