The second generation of consoles was a confusing one, but you have to remember that it was not a jump straight from the Atari 2600 to the NES. Between those you have the Atari 5200, which was not nearly as popular, but it's a middle ground in terms of graphics. Some games were released on all 3 systems, like Mario Bros, so you can get a pretty good idea of how graphics evolved:
Atari 2600
Atari 5200
NES

The first Final Fantasy. I was probably eight or so. I saw it in Nintendo Power before it came out and knew I had to play it. I have no idea why I wanted it so bad, maybe because I had never seen anything like it before. I tried to rent it for months, but it was always out of stock. Finally I got my hands on it, brought it home, and loved it. This was the first RPG I had ever played, and it was a totally new experience for me.

Today I still consider it a pretty good game. It's a fun if fairly simplistic dungeon crawl with solid replay value. I like it a lot more than many of the later entries in the series, that's for sure.

A game that absolutely was a must-have the moment I saw it was Donkey Kong 64. My in-laws had a N64, and I HAD to play that game. I kept going over there every time I could just to play! *laugh* Eventually I bought that system (and the game) from them, and I've played it through at least a dozen times (and no, I'm not exaggerating!)