Ah, I grew up around an old NES, and I loved it before I understood how to actually play it. My older sister bought one with a copy of Super Mario Bros, and she and my brother would play it a lot. I always liked watching Luigi for some reason.
Later on we got Super Mario Bros 3, Dragon Warrior (the original Japanese name is Dragon Quest- a new one came out here not long ago, Dragon Quest VIII), Dragon Warrior II, Dr. Mario, Legacy of the Wizard, and a few other games I remember less about. I know SMB3 was bought as a christmas present, but I think many of the others came from my RPG-loving cousin. My mother and other sister would play them a lot, and somehow they totally amazed me even though half of the game was text I couldn't read well.
In more recent years I've gotten my own NES (I believe the old one was given away) and a number of games for it. My favorites are all four Dragon Warrior games, Final Fantasy, Super Mario Bros. 3, Kirby's Adventure (this game actually rivals SMB3 in my book), old (non-super) Mario Bros, Wrecking Crew (I love the level editor, and the game's an even mix of puzzle and action), Yoshi's Cookie, and Castlevania 2. I guess the RPGness wore off on me a bit
Before getting a NES again though, I got a SNES- before I knew anything about the internet I would spend hours and hours playing it. Super Mario World, Donkey Kong Country, The Legend of Zelda: A Link to the Past... and many, many other games. The SNES is still my favorite system I think. I even got the "Super Scope" bazooka and Yoshi's Safari, and Mario Paint and the mouse for it
Second favorite? Probably my Gameboy SP, but that's thanks to the old gameboy games as much as the Advance games. Super Mario Land and Super Mario Land 2, the Pokemon games (yes the Pokemon games, though I don't bother trying to "catch them all," I just play through and try to find the ones I want for my party), Link's Awakening, and remakes of the Dragon Warrior games... and I'm pretty fond of the newer Castlevania games that are sort of half-RPG, the ones like Symphony of the Night for the playstation, and there's a couple of those in the Gameboy Advance.
Another system I have that I'm pretty fond of is the Virtual Boy
All I really need is a power glove and I'll be set to move into early/mid-'90s video game obscurity land...