NintendoAge is a great website that all NES players should join, if they haven't already. While it is mostly a haven for collectors, it is also home to some of the best gamers you'll find anywhere. Among other things, they are currently teaming up to beat every licensed NES game in existence before the first of the year (10 games to go!). Check out the Gamer's Gauntlet area of the forums to find a host of topics related to everyone's gaming exploits.
This forum is also home to a weekly NES contest. I have participated in this contest a lot this year and have had a blast. And it's soooo easy to participate. Just play the game, take a photo, and post it on the forum thread. Do you not own the game they are playing? No problem, they allow emulators too! For those of you that are used to "official" play where you usually have to videotape yourself, you'll find this to be much more relaxed and a LOT more fun!
The NES contest has just finished 2012 with a bang, by holding a year-end tournament that pitted the year's top players against each other in a series of head-to-head matchups. In each round, players would challenge each other to their favorite games, with the player with the most top scores in each matchup advancing to the next round. This ended up becoming a bit of a grind, but I loved the concept. It also gave me the chance to improve some of my scores on my favorite games!
For the interested, here are the links to the tournament threads (one for each round). The results are posted near the end of each thread.