By far my favourite game for the system is Contra. I've played it for years, and I still can't beat the game without the Konami code (I've come close though). It just defines a platform shooter, basic powerups, infinite ammo, and absolute carnage. I also love the third person view, that was extremely ambitious at the time and it really paid off.
Other games I like are Double Dragon for its beat-em-up style, Metroid for its expansive gameplay and great music, Megaman also for the effective, yet simple gameplay, Mike Tyson's Punchout for its difficulty and novelty and the first 2 Zelda games for just being Zelda. I even liked Silver Surfer for its good gameplay and great soundtrack, even if everyone else hates it for its unfair difficulty.
While the system had many horrific failures (LJN games in particular), it was revolutionary across the world and it had a huge effect on gaming.
While I personally think that the SNES and Wii had even more of an impact due to its library of games and innovation respectively, you still cannot deny that the NES is truly one of the greatest video game consoles of all time.